Daily Papers

Drug discovery can be viewed as a combinatorial search over an immense chemical space, motivating the development of deep generative models for de novo molecular design. Among these, GPT-based molecular language models (MLM) have shown strong molecular design performance by learning chemical syntax and semantics from large-scale data. However, existing MLMs face two fundamental limitations: they inadequately capture the graph-structured nature of molecules when formulated as next-token prediction problems, and they typically lack explicit mechanisms for target-aware generation. Here, we propose SoftMol, a unified framework that co-designs molecular representation, model architecture, and search strategy for target-aware molecular generation. SoftMol introduces soft fragments, a rule-free block representation of SMILES that enables diffusion-native modeling, and develops SoftBD, the first block-diffusion molecular language model that combines local bidirectional diffusion with autoregressive generation under molecular structural constraints. To favor generated molecules with high drug-likeness and synthetic accessibility, SoftBD is trained on a carefully curated dataset named ZINC-Curated. SoftMol further integrates a gated Monte Carlo tree search to assemble fragments in a target-aware manner. Experimental results show that, compared with current state-of-the-art models, SoftMol achieves 100% chemical validity, improves binding affinity by 9.7%, yields a 2-3x increase in molecular diversity, and delivers a 6.6x speedup in inference efficiency. Code is available at https://github.com/szu-aicourse/softmol

Diffusion language models offer unique benefits over autoregressive models due to their potential for parallelized generation and controllability, yet they lag in likelihood modeling and are limited to fixed-length generation. In this work, we introduce a class of block diffusion language models that interpolate between discrete denoising diffusion and autoregressive models. Block diffusion overcomes key limitations of both approaches by supporting flexible-length generation and improving inference efficiency with KV caching and parallel token sampling. We propose a recipe for building effective block diffusion models that includes an efficient training algorithm, estimators of gradient variance, and data-driven noise schedules to minimize the variance. Block diffusion sets a new state-of-the-art performance among diffusion models on language modeling benchmarks and enables generation of arbitrary-length sequences. We provide the code, along with the model weights and blog post on the project page: https://m-arriola.com/bd3lms/

With the emergence of diffusion models as the frontline of generative models, many researchers have proposed molecule generation techniques using conditional diffusion models. However, due to the fundamental nature of a molecule, which carries highly entangled correlations within a small number of atoms and bonds, it becomes difficult for a model to connect raw data with the conditions when the conditions become more complex as natural language. To address this, here we present a novel latent diffusion model dubbed LDMol, which enables a natural text-conditioned molecule generation. Specifically, LDMol is composed of three building blocks: a molecule encoder that produces a chemically informative feature space, a natural language-conditioned latent diffusion model using a Diffusion Transformer (DiT), and an autoregressive decoder for molecule re. In particular, recognizing that multiple SMILES notations can represent the same molecule, we employ a contrastive learning strategy to extract the chemical informative feature space. LDMol not only beats the existing baselines on the text-to-molecule generation benchmark but is also capable of zero-shot inference with unseen scenarios. Furthermore, we show that LDMol can be applied to downstream tasks such as molecule-to-text retrieval and text-driven molecule editing, demonstrating its versatility as a diffusion model.

Diffusion models offer appealing properties for language generation, such as parallel decoding and iterative refinement, but the discrete and highly structured nature of text challenges the direct application of diffusion principles. In this paper, we revisit diffusion language modeling from the view of diffusion process and language modeling, and outline five properties that separate diffusion mechanics from language-specific requirements. We first categorize existing approaches into continuous diffusion in embedding space and discrete diffusion over tokens. We then show that each satisfies only part of the five essential properties and therefore reflects a structural trade-off. Through analyses of recent large diffusion language models, we identify two central issues: (i) uniform corruption does not respect how information is distributed across positions, and (ii) token-wise marginal training cannot capture multi-token dependencies during parallel decoding. These observations motivate diffusion processes that align more closely with the structure of text, and encourage future work toward more coherent diffusion language models.

Molecular generative models, often employing GPT-style language modeling on molecular string representations, have shown promising capabilities when scaled to large datasets and model sizes. However, it remains unclear and subject to debate whether these models adhere to predictable scaling laws under fixed computational budgets, which is a crucial understanding for optimally allocating resources between model size, data volume, and molecular representation. In this study, we systematically investigate the scaling behavior of molecular language models across both pretraining and downstream tasks. We train 300 models and conduct over 10,000 experiments, rigorously controlling compute budgets while independently varying model size, number of training tokens, and molecular representation. Our results demonstrate clear scaling laws in molecular models for both pretraining and downstream transfer, reveal the substantial impact of molecular representation on performance, and explain previously observed inconsistencies in scaling behavior for molecular generation. Additionally, we publicly release the largest library of molecular language models to date to facilitate future research and development. Code and models are available at https://github.com/SZU-ADDG/MLM-Scaling.

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive models, primarily due to their ability to enable parallel decoding. Despite this advantage, most existing DLMs rely on a fixed generation length specified prior to decoding, which restricts their flexibility in real-world applications. While a few recent works attempt to support flexible-length generation, they typically suffer from notable limitations: some require costly retraining to accommodate variable-length outputs, while others depend solely on local confidence signals during decoding. Such local criteria fail to capture the evolving structure of the sequence, often resulting in suboptimal generation quality. In this paper, we propose a training-free, Bayesian structured decoding framework that formulates flexible-length generation as a dynamic structural inference problem. Our approach formulates flexible-length generation as a dynamic structural inference problem, jointly computing the expansion length, the block boundaries, and the decoding schedule. At each window expansion step, the method integrates local uncertainty with structural signals via a unified mechanism that supports dynamic structured generation, including both flexible block expansion and block organization, while maintaining coherence. Extensive experiments across multiple benchmarks demonstrate that our approach significantly improves generation quality and flexibility over existing fixed-length and flexible-length baselines. These results highlight the advantage of Bayesian structured decoding for diffusion language model, providing a principled and efficient solution for structured text generation.

Large language models (LLMs) excel at generation but dominant autoregressive (AR) decoding is inherently sequential, creating a throughput bottleneck. Diffusion Language Models (DLMs)--especially block-wise variants--enable parallel generation and intra-block bidirectional reasoning, yet training large DLMs from scratch is costly and wastes the knowledge in mature AR checkpoints. Prior "adaptation" attempts either modify logits or randomly grow attention masks to full-sequence diffusion, or simply transplant AR weights into a block-diffusion recipe, leaving a fundamental mismatch between AR causality and block-wise bidirectionality unaddressed. We reframe adaptation as a intra-paradigm path from AR to Block-Diffusion by viewing AR as Block-Diffusion with blocksize=1. Concretely, we design the pathway of adaptation as follows: we use a context-causal attention mask (causal in context, bidirectional only within the active block), an efficient parallel adaptation procedure, an auxiliary AR loss to maximize data utilization and retain pretrained knowledge, and gradual increment of the generation block size. The recipe integrates cleanly with masked block-diffusion and maintains train-inference consistency. Built on these components, NBDiff-7B (Base and Instruct) could inherit the long-context modeling and reasoning capabilities, and achieve state-of-the-art performance among the 7B-class DLMs, delivering strong gains on general-knowledge, math, and code benchmarks over strong baselines. These results demonstrate that principled AR-to-block-diffusion adaptation is an effective and compute-efficient alternative to training DLMs from scratch. Codes: https://github.com/YuchuanTian/NBDiff.

One of the most compelling features of global discrete diffusion language models is their global bidirectional contextual capability. However, existing block-based diffusion studies tend to introduce autoregressive priors, which, while offering benefits, can cause models to lose this global coherence at the macro level. To regain global contextual understanding while preserving the advantages of the semi-autoregressive paradigm, we propose Diffusion in Diffusion, a 'draft-then-refine' framework designed to overcome the irreversibility and myopia problems inherent in block diffusion models. Our approach first employs block diffusion to generate rapid drafts using small blocks, then refines these drafts through global bidirectional diffusion with a larger bidirectional receptive field. We utilize snapshot confidence remasking to identify the most critical tokens that require modification, and apply mix-scale training to expand the block diffusion model's global capabilities. Empirical results demonstrate that our approach sets a new benchmark for discrete diffusion models on the OpenWebText dataset. Using only 26% of the fine-tuning budget of baseline models, we reduce generative perplexity from 25.7 to 21.9, significantly narrowing the performance gap with autoregressive models.

Despite a growing interest in diffusion-based language models, existing work has not shown that these models can attain nontrivial likelihoods on standard language modeling benchmarks. In this work, we take the first steps towards closing the likelihood gap between autoregressive and diffusion-based language models, with the goal of building and releasing a diffusion model which outperforms a small but widely-known autoregressive model. We pursue this goal through algorithmic improvements, scaling laws, and increased compute. On the algorithmic front, we introduce several methodological improvements for the maximum-likelihood training of diffusion language models. We then study scaling laws for our diffusion models and find compute-optimal training regimes which differ substantially from autoregressive models. Using our methods and scaling analysis, we train and release Plaid 1B, a large diffusion language model which outperforms GPT-2 124M in likelihood on benchmark datasets and generates fluent samples in unconditional and zero-shot control settings.

Diffusion Language Models (DLMs) are rapidly emerging as a powerful and promising alternative to the dominant autoregressive (AR) paradigm. By generating tokens in parallel through an iterative denoising process, DLMs possess inherent advantages in reducing inference latency and capturing bidirectional context, thereby enabling fine-grained control over the generation process. While achieving a several-fold speed-up, recent advancements have allowed DLMs to show performance comparable to their autoregressive counterparts, making them a compelling choice for various natural language processing tasks. In this survey, we provide a holistic overview of the current DLM landscape. We trace its evolution and relationship with other paradigms, such as autoregressive and masked language models, and cover both foundational principles and state-of-the-art models. Our work offers an up-to-date, comprehensive taxonomy and an in-depth analysis of current techniques, from pre-training strategies to advanced post-training methods. Another contribution of this survey is a thorough review of DLM inference strategies and optimizations, including improvements in decoding parallelism, caching mechanisms, and generation quality. We also highlight the latest approaches to multimodal extensions of DLMs and delineate their applications across various practical scenarios. Furthermore, our discussion addresses the limitations and challenges of DLMs, including efficiency, long-sequence handling, and infrastructure requirements, while outlining future research directions to sustain progress in this rapidly evolving field. Project GitHub is available at https://github.com/VILA-Lab/Awesome-DLMs.

Block-diffusion language models offer a promising path toward faster-than-autoregressive generation by combining block-wise autoregressive decoding with within-block parallel denoising. However, in the few-step regime needed for practical acceleration, standard confidence-thresholded decoding is often brittle: aggressive thresholds hurt quality, while conservative thresholds require unnecessary denoising steps. Existing approaches that address this issue either require additional training or incur extra test-time compute. We present S2D2, a training-free self-speculative decoding framework for block-diffusion language models. Our key observation is that a block-diffusion model becomes autoregressive when the block size is reduced to one, allowing the same pretrained model to act as both drafter and verifier. S2D2 inserts a speculative verification step into standard block-diffusion decoding and uses lightweight routing policies to decide when verification is worth its cost. This yields a hybrid decoding trajectory in which diffusion proposes tokens in parallel, while the autoregressive mode acts as a local sequence-level critic. Across three mainstream block-diffusion families, S2D2 consistently improves the accuracy-speed tradeoff over strong confidence-thresholding baselines. On SDAR, we observe up to 4.7times speedup over autoregressive decoding, and up to 1.57times over a tuned dynamic decoding baseline while improving accuracy by up to 4.5 points. On LLaDA2.1-Mini, S2D2 remains complementary to built-in self-correction, including a conservative setting where it is 4.4times faster than the static baseline with slightly higher accuracy.

Diffusion language models (DLMs) promise parallel, order-agnostic generation, but on standard benchmarks they have historically lagged behind autoregressive models in sample quality and diversity. Recent continuous flow and diffusion approaches over token embeddings have narrowed this gap, suggesting continuous state spaces are highly effective for language. In this work, we further close the autoregressive gap by modeling text as a continuous diffusion process over fixed-width binary bitstreams. Our approach represents semantic tokens as analog bit sequences and utilizes a matched-filter residual parameterization to isolate contextual learning from analytic independent-bit posteriors. Crucially, we adopt a stochastic sampler that applies Langevin-type corrections gated by the entropy-rate profile, automatically concentrating stochasticity in high-information regions while remaining nearly deterministic elsewhere. On the One Billion Word Benchmark (LM1B), our 130M-parameter bitstream model reaches a generative perplexity (GenPPL) of 59.76 at matched real-data entropy (4.31) using 256 neural function evaluations (NFEs), decisively outperforming prior DLM baselines and reaching the autoregressive reference. On OpenWebText (OWT), our stochastic sampler establishes a new continuous-DLM Pareto frontier, achieving GenPPL=27.06 at an entropy of 5.26 using 4times fewer steps than previous 1024-NFE baselines. As an additional architectural benefit, bitstream diffusion removes the O(V) vocabulary scaling bottleneck shared by standard DLMs. By predicting O(log V) bitwise logits via semantic bit-patching, our model yields a reduced memory footprint and higher throughput, demonstrating a scalable paradigm for language generation as vocabulary sizes grow.

Diffusion language models have emerged as a promising approach for text generation. One would naturally expect this method to be an efficient replacement for autoregressive models since multiple tokens can be sampled in parallel during each diffusion step. However, its efficiency-accuracy trade-off is not yet well understood. In this paper, we present a rigorous theoretical analysis of a widely used type of diffusion language model, the Masked Diffusion Model (MDM), and find that its effectiveness heavily depends on the target evaluation metric. Under mild conditions, we prove that when using perplexity as the metric, MDMs can achieve near-optimal perplexity in sampling steps regardless of sequence length, demonstrating that efficiency can be achieved without sacrificing performance. However, when using the sequence error rate--which is important for understanding the "correctness" of a sequence, such as a reasoning chain--we show that the required sampling steps must scale linearly with sequence length to obtain "correct" sequences, thereby eliminating MDM's efficiency advantage over autoregressive models. Our analysis establishes the first theoretical foundation for understanding the benefits and limitations of MDMs. All theoretical findings are supported by empirical studies.

Diffusion-based language models (DLLMs) offer non-sequential, block-wise generation and richer data reuse compared to autoregressive (AR) models, but existing code DLLMs still lag behind strong AR baselines under comparable budgets. We revisit this setting in a controlled study and introduce Stable-DiffCoder, a block diffusion code model that reuses the Seed-Coder architecture, data, and training pipeline. To enable efficient knowledge learning and stable training, we incorporate a block diffusion continual pretraining (CPT) stage enhanced by a tailored warmup and block-wise clipped noise schedule. Under the same data and architecture, Stable-DiffCoder overall outperforms its AR counterpart on a broad suite of code benchmarks. Moreover, relying only on the CPT and supervised fine-tuning stages, Stable-DiffCoder achieves stronger performance than a wide range of \~8B ARs and DLLMs, demonstrating that diffusion-based training can improve code modeling quality beyond AR training alone. Moreover, diffusion-based any-order modeling improves structured code modeling for editing and reasoning, and through data augmentation, benefits low-resource coding languages.

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have recently emerged as a promising alternative. Unfortunately, these models still underperform the autoregressive counterparts, with the performance gap increasing when reducing the number of sampling steps. Our analysis reveals that this degradation is a consequence of an imperfect approximation used by diffusion models. In this work, we propose Energy-based Diffusion Language Model (EDLM), an energy-based model operating at the full sequence level for each diffusion step, introduced to improve the underlying approximation used by diffusion models. More specifically, we introduce an EBM in a residual form, and show that its parameters can be obtained by leveraging a pretrained autoregressive model or by finetuning a bidirectional transformer via noise contrastive estimation. We also propose an efficient generation algorithm via parallel important sampling. Comprehensive experiments on language modeling benchmarks show that our model can consistently outperform state-of-the-art diffusion models by a significant margin, and approaches autoregressive models' perplexity. We further show that, without any generation performance drop, our framework offers a 1.3times sampling speedup over existing diffusion models.

Diffusion Language Models (DLMs) have recently emerged as a strong alternative to autoregressive language models (LMs). DLMs offer comparable accuracy with faster inference speed via parallel decoding. However, standard DLM decoding strategies relying on high-confidence tokens encounter an inherent information-theoretic bottleneck that restricts decoding progress and ultimately slows generation. We demonstrate both theoretically and empirically that prioritizing high-confidence tokens is inherently inefficient. High-probability tokens carry negligible information and strictly relying on them limits the effective progress made in each decoding round. We prove that the number of decoding rounds must grow linearly with the sample's total information (negative log-likelihood) and inversely with the per-round information budget, establishing a bits-to-rounds principle. We also propose Explore-Then-Exploit (ETE), a training-free decoding strategy that maximizes information throughput and decoding efficiency. ETE combines cross-block decoding with targeted exploration of high-uncertainty tokens to reshape the conditional distribution and trigger cascades of confident predictions. Experiments verify our theoretical bounds and demonstrate that ETE consistently reduces the required number of decoding rounds compared to confidence-only baselines without compromising generation quality.

Diffusion language models (DLMs) have strong theoretical efficiency but are limited by fixed-length decoding and incompatibility with key-value (KV) caches. Block diffusion mitigates these issues, yet still enforces a fixed block size and requires expensive training. We introduce Next Sequence Prediction (NSP), which unifies next-token and next-block prediction, enabling the model to adaptively determine the generation length at each step. When the length is fixed to 1, NSP reduces to standard next-token prediction. Building on NSP, we propose Sequential Diffusion Language Model (SDLM), which can retrofit pre-trained autoregressive language models (ALMs) at minimal cost. Specifically, SDLM performs diffusion inference within fixed-size mask blocks, but dynamically decodes consecutive subsequences based on model confidence, thereby preserving KV-cache compatibility and improving robustness to varying uncertainty and semantics across the sequence. Experiments show that SDLM matches or surpasses strong autoregressive baselines using only 3.5M training samples, while achieving 2.1 higher throughput than Qwen-2.5. Notably, the SDLM-32B model delivers even more pronounced efficiency gains, demonstrating the strong scalability potential of our modeling paradigm. Project page and codes: https://github.com/OpenGVLab/SDLM

Although autoregressive models have dominated language modeling in recent years, there has been a growing interest in exploring alternative paradigms to the conventional next-token prediction framework. Diffusion-based language models have emerged as a compelling alternative due to their powerful parallel generation capabilities and inherent editability. However, these models are often constrained by fixed-length generation. A promising direction is to combine the strengths of both paradigms, segmenting sequences into blocks, modeling autoregressive dependencies across blocks while leveraging discrete diffusion to estimate the conditional distribution within each block given the preceding context. Nevertheless, their practical application is often hindered by two key limitations: rigid fixed-length outputs and a lack of flexible control mechanisms. In this work, we address the critical limitations of fixed granularity and weak controllability in current large diffusion language models. We propose CtrlDiff, a dynamic and controllable semi-autoregressive framework that adaptively determines the size of each generation block based on local semantics using reinforcement learning. Furthermore, we introduce a classifier-guided control mechanism tailored to discrete diffusion, which significantly reduces computational overhead while facilitating efficient post-hoc conditioning without retraining. Extensive experiments demonstrate that CtrlDiff sets a new standard among hybrid diffusion models, narrows the performance gap to state-of-the-art autoregressive approaches, and enables effective conditional text generation across diverse tasks.

Diffusion Language Models (DLMs) have emerged as a promising new paradigm for text generative modeling, potentially addressing limitations of autoregressive (AR) models. However, current DLMs have been studied at a smaller scale compared to their AR counterparts and lack fair comparison on language modeling benchmarks. Additionally, training diffusion models from scratch at scale remains challenging. Given the prevalence of open-source AR language models, we propose adapting these models to build text diffusion models. We demonstrate connections between AR and diffusion modeling objectives and introduce a simple continual pre-training approach for training diffusion models. Through systematic evaluation on language modeling, reasoning, and commonsense benchmarks, we show that we can convert AR models ranging from 127M to 7B parameters (GPT2 and LLaMA) into diffusion models DiffuGPT and DiffuLLaMA, using less than 200B tokens for training. Our experimental results reveal that these models outperform earlier DLMs and are competitive with their AR counterparts. We release a suite of DLMs (with 127M, 355M, and 7B parameters) capable of generating fluent text, performing in-context learning, filling in the middle without prompt re-ordering, and following instructions https://github.com/HKUNLP/DiffuLLaMA.

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps. In continuous domains, consistency training along the probability-flow ODE is a popular recipe to accelerate diffusion. For discrete diffusion, no analogous sample-space ODE exists, making direct adaptation ill-defined. We argue that the natural discrete substitute is not a deterministic trajectory but its stochastic counterpart: the exact posterior bridge, available in closed form for broad corruption families including masked and uniform diffusion. Building on this observation, we introduce Multi-Path Discrete Consistency (MPDC), a new principle that trains a denoiser to be path-invariant in expectation across these stochastic bridges, and instantiate it as the Consistent Diffusion Language Model (CDLM), a single-stage, teacher-free training framework. A single CDLM objective unifies masked diffusion, continuous consistency models, and progressive/discrete distillation as analytic limits or empirical approximations of one common view. Empirically, CDLM establishes a new state of the art on both conditional and unconditional text-generation, consistently outperforming strong base discrete diffusion models and often even multi-stage distilled baselines across sampling budgets, with the largest gains in the few-step regime. Together, these results position CDLM as a principled and scalable foundation for the next generation of fast, high-fidelity discrete generative modeling.

Diffusion models have emerged as a powerful paradigm for modern generative modeling, demonstrating strong potential for large language models (LLMs). Unlike conventional autoregressive (AR) models that generate tokens sequentially, diffusion models enable parallel token sampling, leading to faster generation and eliminating left-to-right generation constraints. Despite their empirical success, the theoretical understanding of diffusion model approaches remains underdeveloped. In this work, we develop convergence guarantees for diffusion language models from an information-theoretic perspective. Our analysis demonstrates that the sampling error, measured by the Kullback-Leibler (KL) divergence, decays inversely with the number of iterations T and scales linearly with the mutual information between tokens in the target text sequence. In particular, we establish matching upper and lower bounds, up to some constant factor, to demonstrate the tightness of our convergence analysis. These results offer novel theoretical insights into the practical effectiveness of diffusion language models.

Efficient molecular modeling and design are crucial for the discovery and exploration of novel molecules, and the incorporation of deep learning methods has revolutionized this field. In particular, large language models (LLMs) offer a fresh approach to tackle scientific problems from a natural language processing (NLP) perspective, introducing a research paradigm called scientific language modeling (SLM). However, two key issues remain: how to quantify the match between model and data modalities and how to identify the knowledge-learning preferences of models. To address these challenges, we propose a multi-modal benchmark, named ChEBI-20-MM, and perform 1263 experiments to assess the model's compatibility with data modalities and knowledge acquisition. Through the modal transition probability matrix, we provide insights into the most suitable modalities for tasks. Furthermore, we introduce a statistically interpretable approach to discover context-specific knowledge mapping by localized feature filtering. Our pioneering analysis offers an exploration of the learning mechanism and paves the way for advancing SLM in molecular science.

Chemical language models (CLMs) have emerged as promising competitors to popular classical machine learning models for molecular property prediction (MPP) tasks. However, an increasing number of studies have reported inconsistent and contradictory results for the performance of CLMs across various MPP benchmark tasks. In this study, we conduct and analyze hundreds of meticulously controlled experiments to systematically investigate the effects of various factors, such as dataset size, model size, and standardization, on the pre-training and fine-tuning performance of CLMs for MPP. In the absence of well-established scaling laws for encoder-only masked language models, our aim is to provide comprehensive numerical evidence and a deeper understanding of the underlying mechanisms affecting the performance of CLMs for MPP tasks, some of which appear to be entirely overlooked in the literature.

Autoregressive language models (ARMs) deliver strong likelihoods, but are inherently serial: they generate one token per forward pass, which limits throughput and inflates latency for long sequences. Diffusion Language Models (DLMs) parallelize across positions and thus appear promising for language generation, yet standard discrete diffusion typically needs hundreds to thousands of model evaluations to reach high quality, trading serial depth for iterative breadth. We introduce FS-DFM, Few-Step Discrete Flow-Matching. A discrete flow-matching model designed for speed without sacrificing quality. The core idea is simple: make the number of sampling steps an explicit parameter and train the model to be consistent across step budgets, so one big move lands where many small moves would. We pair this with a reliable update rule that moves probability in the right direction without overshooting, and with strong teacher guidance distilled from long-run trajectories. Together, these choices make few-step sampling stable, accurate, and easy to control. On language modeling benchmarks, FS-DFM with 8 sampling steps achieves perplexity parity with a 1,024-step discrete-flow baseline for generating 1,024 tokens using a similar-size model, delivering up to 128 times faster sampling and corresponding latency/throughput gains.

Modern LLM pre-training consumes vast amounts of compute and training data, making the scaling behavior, or scaling laws, of different models a key distinguishing factor. Discrete diffusion language models (DLMs) have been proposed as an alternative to autoregressive language models (ALMs). However, their scaling behavior has not yet been fully explored, with prior work suggesting that they require more data and compute to match the performance of ALMs. We study the scaling behavior of DLMs on different noise types by smoothly interpolating between masked and uniform diffusion while paying close attention to crucial hyperparameters such as batch size and learning rate. Our experiments reveal that the scaling behavior of DLMs strongly depends on the noise type and is considerably different from ALMs. While all noise types converge to similar loss values in compute-bound scaling, we find that uniform diffusion requires more parameters and less data for compute-efficient training compared to masked diffusion, making them a promising candidate in data-bound settings. We scale our uniform diffusion model up to 10B parameters trained for 10^{22} FLOPs, confirming the predicted scaling behavior and making it the largest publicly known uniform diffusion model to date.

Diffusion language models (DLMs) have recently emerged as a strong alternative to autoregressive models by enabling parallel text generation. To improve inference efficiency and KV-cache compatibility, prior work commonly adopts block-based diffusion, decoding tokens block by block. However, this paradigm suffers from a structural limitation that we term Boundary-Induced Context Truncation (BICT): undecoded tokens near block boundaries are forced to commit without access to nearby future context, even when such context could substantially reduce uncertainty. This limitation degrades decoding certainty and generation quality, especially for tasks requiring precise reasoning, such as mathematical problem solving and code generation. We propose Deferred Commitment Decoding (DCD), a novel, training-free decoding strategy that mitigates this issue. DCD maintains a certainty-aware sliding window over masked tokens, resolving low-uncertainty tokens early while deferring high-uncertainty tokens until sufficient contextual evidence becomes available. Extensive experiments across multiple diffusion language models, benchmarks, and caching configurations show that DCD improves generation accuracy by 1.73% with comparable time on average compared to fixed block-based diffusion methods, with the most significant improvement reaching 16.5%. These results demonstrate that deferring token commitment based on uncertainty is a simple yet effective principle for improving both the quality and efficiency of diffusion language model decoding.

Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized distribution, which is less expressive than AR. Recent Flow Language Models (FLMs) apply continuous flows to language, transporting noise to data with a deterministic ODE that avoids factorized sampling. FLMs operate on one-hot vectors whose dimension scales with the vocabulary size, making FLMs costly to train. Moreover, since all distinct one-hot embeddings are equidistant in ell_2, adding Gaussian noise does not have a clear semantic interpretation (unlike images, where Gaussian noise progressively degrades structure). We introduce S-FLM, a latent FLM in the hypersphere. S-FLM generates sequences by rotating vectors in S^{d-1} along a velocity field learned with cross-entropy, avoiding the overhead of materializing one-hot vectors. Previous FLMs match AR in Generative Perplexity (Gen.\ PPL), but samples with high likelihood are not necessarily correct in verifiable domains such as math and code. S-FLM substantially improves continuous flow language models on large-vocabulary reasoning and closes the gap to masked diffusion under standard-temperature sampling (T=1), while a gap remains under optimized low-temperature (T=0.1) decoding.

Diffusion language models are a promising alternative to autoregressive models due to their potential for faster generation. Among discrete diffusion approaches, Masked diffusion currently dominates, largely driven by strong perplexity on language modeling benchmarks. In this work, we present the first scaling law study of uniform-state and interpolating discrete diffusion methods. We also show that Masked diffusion models can be made approximately 12% more FLOPs-efficient when trained with a simple cross-entropy objective. We find that perplexity is informative within a diffusion family but can be misleading across families, where models with worse likelihood scaling may be preferable due to faster and more practical sampling, as reflected by the speed-quality Pareto frontier. These results challenge the view that Masked diffusion is categorically the future of diffusion language modeling and that perplexity alone suffices for cross-algorithm comparison. Scaling all methods to 1.7B parameters, we show that uniform-state diffusion remains competitive on likelihood-based benchmarks and outperforms autoregressive and Masked diffusion models on GSM8K, despite worse validation perplexity. We provide the code, model checkpoints, and video tutorials on the project page: http://s-sahoo.github.io/scaling-dllms

Recently, diffusion models have emerged as a new paradigm for generative models. Despite the success in domains using continuous signals such as vision and audio, adapting diffusion models to natural language is under-explored due to the discrete nature of texts, especially for conditional generation. We tackle this challenge by proposing DiffuSeq: a diffusion model designed for sequence-to-sequence (Seq2Seq) text generation tasks. Upon extensive evaluation over a wide range of Seq2Seq tasks, we find DiffuSeq achieving comparable or even better performance than six established baselines, including a state-of-the-art model that is based on pre-trained language models. Apart from quality, an intriguing property of DiffuSeq is its high diversity during generation, which is desired in many Seq2Seq tasks. We further include a theoretical analysis revealing the connection between DiffuSeq and autoregressive/non-autoregressive models. Bringing together theoretical analysis and empirical evidence, we demonstrate the great potential of diffusion models in complex conditional language generation tasks. Code is available at https://github.com/Shark-NLP/DiffuSeq

Diffusion language models (DLMs) have recently emerged as a compelling alternative to autoregressive generation, offering parallel generation and improved global coherence. During inference, DLMs generate text by iteratively denoising masked sequences in parallel; however, determining which positions to unmask and which tokens to commit forms a large combinatorial search problem. Existing inference methods approximate this search using heuristics, which often yield suboptimal decoding paths; other approaches instead rely on additional training to guide token selection. To introduce a principled search mechanism for DLMs inference, we introduce MEDAL, a framework that integrates Monte Carlo Tree SEarch initialization for Diffusion LAnguage Model inference. We employ Monte Carlo Tree Search at the initialization stage to explore promising unmasking trajectories, providing a robust starting point for subsequent refinement. This integration is enabled by restricting the search space to high-confidence actions and prioritizing token choices that improve model confidence over remaining masked positions. Across multiple benchmarks, MEDAL achieves up to 22.0% improvement over existing inference strategies, establishing a new paradigm for search-based inference in diffusion language models.

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. Yet diffusion models that directly work on discrete data space do not fully exploit the power of iterative refinement, as the signals are lost during the transition between discrete states. Existing continuous diffusion models for discrete data have limited performance compared to discrete approaches, and the unclear link between them restricts the development of diffusion models for discrete data. In this work, we propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution. We establish a connection between the discrete diffusion and continuous flow on the statistical manifold, and building on the analogy, we introduce a simple design for the diffusion process that generalizes previous discrete diffusion models. We further propose a simulation-free training framework based on radial symmetry and a simple technique to address the high dimensionality of the manifold. Comprehensive experiments on language modeling benchmarks and other modalities show that our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models. Codes available at https://github.com/harryjo97/RDLM{https://github.com/harryjo97/RDLM}.

Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive (AR) models, offering sub-linear generation latency and bidirectional capabilities that are particularly appealing for code generation and editing. Achieving sub-linear latency in discrete DLMs requires predicting multiple tokens in parallel. However, standard DLMs sample tokens independently from conditional marginal distributions, failing to capture the joint dependencies among concurrently generated tokens. As a result, they often lead to syntactic inconsistencies and break multi-token structures. In this work, we introduce CoDiLA (Coherent Diffusion with Local Autoregression), a method that reconciles parallel sampling with local dependency modeling. Rather than forcing the DLM to resolve fine-grained syntax, CoDiLA delegates local decoding to a small, auxiliary AR model operating on the diffusion latents. This design allows for parallel block generation while ensuring sequential validity within each block and maintaining core DLM capabilities, including bidirectional modeling across blocks. We demonstrate that using a highly compact auxiliary AR model (e.g., 0.6B parameters) effectively eliminates coherence artifacts, establishing a new Pareto frontier for accuracy and speed in code generation benchmarks.

Discrete diffusion models enable parallel token sampling for faster inference than autoregressive approaches. However, prior diffusion models use a decoder-only architecture, which requires sampling algorithms that invoke the full network at every denoising step and incur high computational cost. Our key insight is that discrete diffusion models perform two types of computation: 1) representing clean tokens and 2) denoising corrupted tokens, which enables us to use separate modules for each task. We propose an encoder-decoder architecture to accelerate discrete diffusion inference, which relies on an encoder to represent clean tokens and a lightweight decoder to iteratively refine a noised sequence. We also show that this architecture enables faster training of block diffusion models, which partition sequences into blocks for better quality and are commonly used in diffusion language model inference. We introduce a framework for Efficient Encoder-Decoder Diffusion (E2D2), consisting of an architecture with specialized training and sampling algorithms, and we show that E2D2 achieves superior trade-offs between generation quality and inference throughput on summarization, translation, and mathematical reasoning tasks. We provide the code, model weights, and blog post on the project page: https://m-arriola.com/e2d2

Despite their ability to understand chemical knowledge, large language models (LLMs) remain limited in their capacity to propose novel molecules with desired functions (e.g., drug-like properties). In addition, the molecules that LLMs propose can often be challenging to make, and are almost never compatible with automated synthesis approaches. To better enable the discovery of functional small molecules, LLMs need to learn a new molecular language that is more effective in predicting properties and inherently synced with automated synthesis technology. Current molecule LLMs are limited by representing molecules based on atoms. In this paper, we argue that just like tokenizing texts into meaning-bearing (sub-)word tokens instead of characters, molecules should be tokenized at the level of functional building blocks, i.e., parts of molecules that bring unique functions and serve as effective building blocks for real-world automated laboratory synthesis. This motivates us to propose mCLM, a modular Chemical-Language Model that comprises a bilingual language model that understands both natural language descriptions of functions and molecular blocks. mCLM front-loads synthesizability considerations while improving the predicted functions of molecules in a principled manner. mCLM, with only 3B parameters, achieves improvements in synthetic accessibility relative to 7 other leading generative AI methods including GPT-5. When tested on 122 out-of-distribution medicines using only building blocks/tokens that are compatible with automated modular synthesis, mCLM outperforms all baselines in property scores and synthetic accessibility. mCLM can also reason on multiple functions and iteratively self-improve to rescue drug candidates that failed late in clinical trials ("fallen angels").

Diffusion models have achieved great success in modeling continuous data modalities such as images, audio, and video, but have seen limited use in discrete domains such as language. Recent attempts to adapt diffusion to language have presented diffusion as an alternative to autoregressive language generation. We instead view diffusion as a complementary method that can augment the generative capabilities of existing pre-trained language models. We demonstrate that continuous diffusion models can be learned in the latent space of a pre-trained encoder-decoder model, enabling us to sample continuous latent representations that can be decoded into natural language with the pre-trained decoder. We show that our latent diffusion models are more effective at sampling novel text from data distributions than a strong autoregressive baseline and also enable controllable generation.

While diffusion models excel at generating high-quality images, prior work reports a significant performance gap between diffusion and autoregressive (AR) methods in language modeling. In this work, we show that simple masked discrete diffusion is more performant than previously thought. We apply an effective training recipe that improves the performance of masked diffusion models and derive a simplified, Rao-Blackwellized objective that results in additional improvements. Our objective has a simple form -- it is a mixture of classical masked language modeling losses -- and can be used to train encoder-only language models that admit efficient samplers, including ones that can generate arbitrary lengths of text semi-autoregressively like a traditional language model. On language modeling benchmarks, a range of masked diffusion models trained with modern engineering practices achieves a new state-of-the-art among diffusion models, and approaches AR perplexity. We release our code at: https://github.com/kuleshov-group/mdlm

Diffusion-based large language models (Diffusion LLMs) have shown promise for non-autoregressive text generation with parallel decoding capabilities. However, the practical inference speed of open-sourced Diffusion LLMs often lags behind autoregressive models due to the lack of Key-Value (KV) Cache and quality degradation when decoding multiple tokens simultaneously. To bridge this gap, we introduce a novel block-wise approximate KV Cache mechanism tailored for bidirectional diffusion models, enabling cache reuse with negligible performance drop. Additionally, we identify the root cause of generation quality degradation in parallel decoding as the disruption of token dependencies under the conditional independence assumption. To address this, we propose a confidence-aware parallel decoding strategy that selectively decodes tokens exceeding a confidence threshold, mitigating dependency violations and maintaining generation quality. Experimental results on LLaDA and Dream models across multiple LLM benchmarks demonstrate up to 27.6times throughput improvement with minimal accuracy loss, closing the performance gap with autoregressive models and paving the way for practical deployment of Diffusion LLMs.

This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to develop a family of reparameterized discrete diffusion models. The derived generic framework is highly flexible, offers a fresh perspective of the generation process in discrete diffusion models, and features more effective training and decoding techniques. We conduct extensive experiments to evaluate the text generation capability of our model, demonstrating significant improvements over existing diffusion models.

Language-molecule models have emerged as an exciting direction for molecular discovery and understanding. However, training these models is challenging due to the scarcity of molecule-language pair datasets. At this point, datasets have been released which are 1) small and scraped from existing databases, 2) large but noisy and constructed by performing entity linking on the scientific literature, and 3) built by converting property prediction datasets to natural language using templates. In this document, we detail the L+M-24 dataset, which has been created for the Language + Molecules Workshop shared task at ACL 2024. In particular, L+M-24 is designed to focus on three key benefits of natural language in molecule design: compositionality, functionality, and abstraction.

Diffusion large language models (dLLMs) have emerged as a promising alternative for text generation, distinguished by their native support for parallel decoding. In practice, block inference is crucial for avoiding order misalignment in global bidirectional decoding and improving output quality. However, the widely-used fixed, predefined block (naive) schedule is agnostic to semantic difficulty, making it a suboptimal strategy for both quality and efficiency: it can force premature commitments to uncertain positions while delaying easy positions near block boundaries. In this work, we analyze the limitations of naive block scheduling and disclose the importance of dynamically adapting the schedule to semantic difficulty for reliable and efficient inference. Motivated by this, we propose Dynamic Sliding Block (DSB), a training-free block scheduling method that uses a sliding block with a dynamic size to overcome the rigidity of the naive block. To further improve efficiency, we introduce DSB Cache, a training-free KV-cache mechanism tailored to DSB. Extensive experiments across multiple models and benchmarks demonstrate that DSB, together with DSB Cache, consistently improves both generation quality and inference efficiency for dLLMs. Code is released at https://github.com/lizhuo-luo/DSB.

The integration of molecule and language has garnered increasing attention in molecular science. Recent advancements in Language Models (LMs) have demonstrated potential for the comprehensive modeling of molecule and language. However, existing works exhibit notable limitations. Most existing works overlook the modeling of 3D information, which is crucial for understanding molecular structures and also functions. While some attempts have been made to leverage external structure encoding modules to inject the 3D molecular information into LMs, there exist obvious difficulties that hinder the integration of molecular structure and language text, such as modality alignment and separate tuning. To bridge this gap, we propose 3D-MolT5, a unified framework designed to model both 1D molecular sequence and 3D molecular structure. The key innovation lies in our methodology for mapping fine-grained 3D substructure representations (based on 3D molecular fingerprints) to a specialized 3D token vocabulary for 3D-MolT5. This 3D structure token vocabulary enables the seamless combination of 1D sequence and 3D structure representations in a tokenized format, allowing 3D-MolT5 to encode molecular sequence (SELFIES), molecular structure, and text sequences within a unified architecture. Alongside, we further introduce 1D and 3D joint pre-training to enhance the model's comprehension of these diverse modalities in a joint representation space and better generalize to various tasks for our foundation model. Through instruction tuning on multiple downstream datasets, our proposed 3D-MolT5 shows superior performance than existing methods in molecular property prediction, molecule captioning, and text-based molecule generation tasks. Our code will be available on GitHub soon.

The success of language models, especially transformer-based architectures, has trickled into other domains giving rise to "scientific language models" that operate on small molecules, proteins or polymers. In chemistry, language models contribute to accelerating the molecule discovery cycle as evidenced by promising recent findings in early-stage drug discovery. Here, we review the role of language models in molecular discovery, underlining their strength in de novo drug design, property prediction and reaction chemistry. We highlight valuable open-source software assets thus lowering the entry barrier to the field of scientific language modeling. Last, we sketch a vision for future molecular design that combines a chatbot interface with access to computational chemistry tools. Our contribution serves as a valuable resource for researchers, chemists, and AI enthusiasts interested in understanding how language models can and will be used to accelerate chemical discovery.

Diffusion Language Models (DLMs) present a promising non-sequential paradigm for text generation, distinct from standard autoregressive (AR) approaches. However, current decoding strategies often adopt a reactive stance, underutilizing the global bidirectional context to dictate global trajectories. To address this, we propose Plan-Verify-Fill (PVF), a training-free paradigm that grounds planning via quantitative validation. PVF actively constructs a hierarchical skeleton by prioritizing high-leverage semantic anchors and employs a verification protocol to operationalize pragmatic structural stopping where further deliberation yields diminishing returns. Extensive evaluations on LLaDA-8B-Instruct and Dream-7B-Instruct demonstrate that PVF reduces the Number of Function Evaluations (NFE) by up to 65% compared to confidence-based parallel decoding across benchmark datasets, unlocking superior efficiency without compromising accuracy.

Diffusion language models (DLMs) have shown strong potential for general natural language tasks with in-context examples. However, due to the bidirectional attention mechanism, DLMs incur substantial computational cost as context length increases. This work addresses this issue with a key discovery: unlike the sequential generation in autoregressive language models (ARLMs), the diffusion generation paradigm in DLMs allows efficient dynamic adjustment of the context during generation. Building on this insight, we propose Dynamic In-Context Planner (DIP), a context-optimization method that dynamically selects and inserts in-context examples during generation, rather than providing all examples in the prompt upfront. Results show DIP maintains generation quality while achieving up to 12.9times inference speedup over standard inference and 1.17times over KV cache-enhanced inference.

Designing de-novo molecules with desired property profiles requires efficient exploration of the vast chemical space ranging from 10^{23} to 10^{60} possible synthesizable candidates. While various deep generative models have been developed to design small molecules using diverse input representations, Molecular Large Language Models (Mol-LLMs) based on string representations have emerged as a scalable approach capable of exploring billions of molecules. However, there remains limited understanding regarding how standard language modeling practices such as textual representations, tokenization strategies, model size, and dataset scale impact molecular generation performance. In this work, we systematically investigate these critical aspects by introducing NovoMolGen, a family of transformer-based foundation models pretrained on 1.5 billion molecules for de-novo molecule generation. Through extensive empirical analyses, we identify a weak correlation between performance metrics measured during pretraining and actual downstream performance, revealing important distinctions between molecular and general NLP training dynamics. NovoMolGen establishes new state-of-the-art results, substantially outperforming prior Mol-LLMs and specialized generative models in both unconstrained and goal-directed molecular generation tasks, thus providing a robust foundation for advancing efficient and effective molecular modeling strategies.

Proteins are fundamental to biology, executing diverse functions through complex physicochemical interactions, and they hold transformative potential across medicine, materials science, and environmental applications. Protein Language Models (pLMs) aim to unlock insights from the vast space of unlabeled protein sequences by learning rich, semantic representations from primary sequences via masked language modeling. However, these models typically exhibit limited generative capacity. In this work, we introduce the Diffusion Sequence Model (DSM), a novel pLM trained with masked diffusion to enable both high-quality representation learning and generative protein design. DSM builds upon the ESM2 architecture by incorporating a masked forward diffusion process inspired by the LLaDA framework. After training, DSM is capable of generating diverse, biomimetic sequences that align with expected amino acid compositions, secondary structures, and predicted functions, even with 90\% token corruption. Furthermore, DSM's learned representations match or exceed those of similarly sized pLMs on downstream tasks. We also introduce DSM(ppi), a variant fine-tuned to generate protein binders by attending to target sequences. We demonstrate DSM(ppi)'s effectiveness on the challenging Bench-tested Binder Benchmark (BenchBB), where both DSM and DSM(ppi) produce candidates with superior predicted binding affinity compared to known binders. Our results establish masked diffusion as a powerful paradigm for unifying protein representation and generation in a single framework.

Optical Character Recognition (OCR) is a fundamental task for digitizing information, serving as a critical bridge between visual data and textual understanding. While modern Vision-Language Models (VLM) have achieved high accuracy in this domain, they predominantly rely on autoregressive decoding, which becomes computationally expensive and slow for long documents as it requires a sequential forward pass for every generated token. We identify a key opportunity to overcome this bottleneck: unlike open-ended generation, OCR is a highly deterministic task where the visual input strictly dictates a unique output sequence, theoretically enabling efficient, parallel decoding via diffusion models. However, we show that existing masked diffusion models fail to harness this potential; those introduce structural instabilities that are benign in flexible tasks, like captioning, but catastrophic for the rigid, exact-match requirements of OCR. To bridge this gap, we introduce DODO, the first VLM to utilize block discrete diffusion and unlock its speedup potential for OCR. By decomposing generation into blocks, DODO mitigates the synchronization errors of global diffusion. Empirically, our method achieves near state-of-the-art accuracy while enabling up to 3x faster inference compared to autoregressive baselines.

Large language models (LLMs) are introducing a paradigm shift in molecular discovery by enabling text-guided interaction with chemical spaces through natural language, symbolic notations, with emerging extensions to incorporate multi-modal inputs. To advance the new field of LLM for molecular discovery, this survey provides an up-to-date and forward-looking review of the emerging use of LLMs for two central tasks: molecule generation and molecule optimization. Based on our proposed taxonomy for both problems, we analyze representative techniques in each category, highlighting how LLM capabilities are leveraged across different learning settings. In addition, we include the commonly used datasets and evaluation protocols. We conclude by discussing key challenges and future directions, positioning this survey as a resource for researchers working at the intersection of LLMs and molecular science. A continuously updated reading list is available at https://github.com/REAL-Lab-NU/Awesome-LLM-Centric-Molecular-Discovery.

In recent years, groundbreaking advancements in natural language processing have culminated in the emergence of powerful large language models (LLMs), which have showcased remarkable capabilities across a vast array of domains, including the understanding, generation, and translation of natural language, and even tasks that extend beyond language processing. In this report, we delve into the performance of LLMs within the context of scientific discovery, focusing on GPT-4, the state-of-the-art language model. Our investigation spans a diverse range of scientific areas encompassing drug discovery, biology, computational chemistry (density functional theory (DFT) and molecular dynamics (MD)), materials design, and partial differential equations (PDE). Evaluating GPT-4 on scientific tasks is crucial for uncovering its potential across various research domains, validating its domain-specific expertise, accelerating scientific progress, optimizing resource allocation, guiding future model development, and fostering interdisciplinary research. Our exploration methodology primarily consists of expert-driven case assessments, which offer qualitative insights into the model's comprehension of intricate scientific concepts and relationships, and occasionally benchmark testing, which quantitatively evaluates the model's capacity to solve well-defined domain-specific problems. Our preliminary exploration indicates that GPT-4 exhibits promising potential for a variety of scientific applications, demonstrating its aptitude for handling complex problem-solving and knowledge integration tasks. Broadly speaking, we evaluate GPT-4's knowledge base, scientific understanding, scientific numerical calculation abilities, and various scientific prediction capabilities.

Controlling the behavior of language models (LMs) without re-training is a major open problem in natural language generation. While recent works have demonstrated successes on controlling simple sentence attributes (e.g., sentiment), there has been little progress on complex, fine-grained controls (e.g., syntactic structure). To address this challenge, we develop a new non-autoregressive language model based on continuous diffusions that we call Diffusion-LM. Building upon the recent successes of diffusion models in continuous domains, Diffusion-LM iteratively denoises a sequence of Gaussian vectors into word vectors, yielding a sequence of intermediate latent variables. The continuous, hierarchical nature of these intermediate variables enables a simple gradient-based algorithm to perform complex, controllable generation tasks. We demonstrate successful control of Diffusion-LM for six challenging fine-grained control tasks, significantly outperforming prior work.

Diffusion language models (DLMs) have recently emerged as an alternative to autoregressive approaches, offering parallel sequence generation and flexible token orders. However, their inference remains slower than that of autoregressive models, primarily due to the cost of bidirectional attention and the large number of refinement steps required for high quality outputs. In this work, we highlight and leverage an overlooked property of DLMs early answer convergence: in many cases, the correct answer can be internally identified by half steps before the final decoding step, both under semi-autoregressive and random remasking schedules. For example, on GSM8K and MMLU, up to 97% and 99% of instances, respectively, can be decoded correctly using only half of the refinement steps. Building on this observation, we introduce Prophet, a training-free fast decoding paradigm that enables early commit decoding. Specifically, Prophet dynamically decides whether to continue refinement or to go "all-in" (i.e., decode all remaining tokens in one step), using the confidence gap between the top-2 prediction candidates as the criterion. It integrates seamlessly into existing DLM implementations, incurs negligible overhead, and requires no additional training. Empirical evaluations of LLaDA-8B and Dream-7B across multiple tasks show that Prophet reduces the number of decoding steps by up to 3.4x while preserving high generation quality. These results recast DLM decoding as a problem of when to stop sampling, and demonstrate that early decode convergence provides a simple yet powerful mechanism for accelerating DLM inference, complementary to existing speedup techniques. Our code is publicly available at https://github.com/pixeli99/Prophet.

Continuous diffusion has been the foundation of high-fidelity, controllable, and few-step generation of many data modalities such as images. However, in language modeling, prior continuous diffusion language models (DLMs) lag behind discrete counterparts due to the sparse data space and the underexplored design space. In this work, we close this gap with LangFlow, the first continuous DLM to rival discrete diffusion, by connecting embedding-space DLMs to Flow Matching via Bregman divergence, alongside three key innovations: (1) we derive a novel ODE-based NLL bound for principled evaluation of continuous flow-based language models; (2) we propose an information-uniform principle for setting the noise schedule, which motivates a learnable noise scheduler based on a Gumbel distribution; and (3) we revise prior training protocols by incorporating self-conditioning, as we find it improves both likelihood and sample quality of embedding-space DLMs with effects substantially different from discrete diffusion. Putting everything together, LangFlow rivals top discrete DLMs on both the perplexity (PPL) and the generative perplexity (Gen. PPL), reaching a PPL of 30.0 on LM1B and 24.6 on OpenWebText. It even exceeds autoregressive baselines in zero-shot transfer on 4 out of 7 benchmarks. LangFlow provides the first clear evidence that continuous diffusion is a promising paradigm for language modeling. Homepage: https://github.com/nealchen2003/LangFlow

Recently, diffusion models have garnered significant interest in the field of text processing due to their many potential advantages compared to conventional autoregressive models. In this work, we propose Diffusion-of-Thought (DoT), a novel approach that integrates diffusion models with Chain-of-Thought, a well-established technique for improving the reasoning ability of autoregressive language models. In contrast to autoregressive language models that make decisions in a left-to-right, token-by-token manner, DoT allows reasoning steps to diffuse over time through a diffusion language model and offers greater flexibility in trading-off computation for reasoning performance. Our experimental results demonstrate the effectiveness of DoT in multi-digit multiplication, boolean logic, and grade school math problems, with a small diffusion model outperforming a much larger autoregressive model in both efficiency and accuracy. In addition to that, DoT showcases promising self-correction abilities and benefits from existing reasoning-enhancing techniques like self-consistency decoding. Our findings contribute to the understanding and development of reasoning with diffusion language models.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Unlike autoregressive language models, which terminate variable-length generation upon predicting an End-of-Sequence (EoS) token, Diffusion Language Models (DLMs) operate over a fixed maximum-length context window for a predetermined number of denoising steps. However, this process is independent of the required response length, resulting in computational waste for the majority of short responses common in reasoning and chat tasks. To address this problem, we conjecture that the latent prompt representation contains sufficient information to estimate the required output length. We provide empirical evidence for this phenomenon and propose a zero-shot mechanism to dynamically crop the context window before generation begins, leading to fewer diffusion steps and substantial computational savings. We evaluate our approach on four benchmarks with diverse tasks -- GSM8K (reasoning), HumanEval (code generation), IfEval (instruction following), and LongFormQA (question answering) -- revealing massive efficiency gains at minimal performance impact. We report significant reductions in FLOPs across all tasks, with no statistically significant performance degradation, and significant performance improvements in 2 out of 4 tasks.

Uniform-state discrete diffusion models hold the promise of fast text generation due to their inherent ability to self-correct. However, they are typically outperformed by autoregressive models and masked diffusion models. In this work, we narrow this performance gap by leveraging a key insight: Uniform-state diffusion processes naturally emerge from an underlying Gaussian diffusion. Our method, Duo, transfers powerful techniques from Gaussian diffusion to improve both training and sampling. First, we introduce a curriculum learning strategy guided by the Gaussian process, doubling training speed by reducing variance. Models trained with curriculum learning surpass autoregressive models in zero-shot perplexity on 3 of 7 benchmarks. Second, we present Discrete Consistency Distillation, which adapts consistency distillation from the continuous to the discrete setting. This algorithm unlocks few-step generation in diffusion language models by accelerating sampling by two orders of magnitude. We provide the code and model checkpoints on the project page: http://s-sahoo.github.io/duo

Diverse outputs in text generation are necessary for effective exploration in complex reasoning tasks, such as code generation and mathematical problem solving. Such Pass@k problems benefit from distinct candidates covering the solution space. However, traditional sampling approaches often waste computational resources on repetitive failure modes. While Diffusion Language Models have emerged as a competitive alternative to the prevailing Autoregressive paradigm, they remain susceptible to this redundancy, with independent samples frequently collapsing into similar modes. To address this, we propose a training free, low cost intervention to enhance generative diversity in Diffusion Language Models. Our approach modifies intermediate samples in a batch sequentially, where each sample is repelled from the feature space of previous samples, actively penalising redundancy. Unlike prior methods that require retraining or beam search, our strategy incurs negligible computational overhead, while ensuring that each sample contributes a unique perspective to the batch. We evaluate our method on the HumanEval and GSM8K benchmarks using the LLaDA-8B-Instruct model. Our results demonstrate significantly improved diversity and Pass@k performance across various temperature settings. As a simple modification to the sampling process, our method offers an immediate, low-cost improvement for current and future Diffusion Language Models in tasks that benefit from diverse solution search. We make our code available at https://github.com/sean-lamont/odd.

Recent advancements in large language models have opened new possibilities for generative molecular drug design. We present Chemlactica and Chemma, two language models fine-tuned on a novel corpus of 110M molecules with computed properties, totaling 40B tokens. These models demonstrate strong performance in generating molecules with specified properties and predicting new molecular characteristics from limited samples. We introduce a novel optimization algorithm that leverages our language models to optimize molecules for arbitrary properties given limited access to a black box oracle. Our approach combines ideas from genetic algorithms, rejection sampling, and prompt optimization. It achieves state-of-the-art performance on multiple molecular optimization benchmarks, including an 8% improvement on Practical Molecular Optimization compared to previous methods. We publicly release the training corpus, the language models and the optimization algorithm.

In this work, we provide a systematic survey of Discrete Diffusion Language Models (dLLMs) and Discrete Diffusion Multimodal Language Models (dMLLMs). Unlike autoregressive (AR) models, dLLMs and dMLLMs adopt a multi-token, parallel decoding paradigm using full attention and a denoising-based generation strategy. This paradigm naturally enables parallel generation, fine-grained output controllability, and dynamic, response-aware perception. These capabilities are previously difficult to achieve with AR models. Recently, a growing number of industrial-scale proprietary d(M)LLMs, as well as a large number of open-source academic d(M)LLMs, have demonstrated performance comparable to their autoregressive counterparts, while achieving up to 10x acceleration in inference speed. The advancement of discrete diffusion LLMs and MLLMs has been largely driven by progress in two domains. The first is the development of autoregressive LLMs and MLLMs, which has accumulated vast amounts of data, benchmarks, and foundational infrastructure for training and inference. The second contributing domain is the evolution of the mathematical models underlying discrete diffusion. Together, these advancements have catalyzed a surge in dLLMs and dMLLMs research in early 2025. In this work, we present a comprehensive overview of the research in the dLLM and dMLLM domains. We trace the historical development of dLLMs and dMLLMs, formalize the underlying mathematical frameworks, and categorize representative models. We further analyze key techniques for training and inference, and summarize emerging applications across language, vision-language, and biological domains. We conclude by discussing future directions for research and deployment. Paper collection: https://github.com/LiQiiiii/DLLM-Survey

Recent advances in block diffusion language models have demonstrated competitive performance and strong scalability on reasoning tasks. However, existing BDLMs have limited exploration under the test-time scaling setting and face more severe decoding challenges in long Chain-of-Thought reasoning, particularly in balancing the decoding speed and effectiveness. In this work, we propose a unified framework for test-time scaling in BDLMs that introduces adaptivity in both decoding and block-wise generation. At the decoding level, we propose Bounded Adaptive Confidence Decoding (BACD), a difficulty-aware sampling strategy that dynamically adjusts denoising based on model confidence, accelerating inference while controlling error accumulation. Beyond step-wise adaptivity, we introduce Think Coarse, Critic Fine (TCCF), a test-time scaling paradigm that allocates large block sizes to exploratory reasoning and smaller block sizes to refinement, achieving an effective efficiency-effectiveness balance. To enable efficient and effective decoding with a large block size, we adopt Progressive Block Size Extension, which mitigates performance degradation when scaling block sizes. Extensive experiments show that applying BACD and TCCF to TDAR-8B yields significant improvements over strong baselines such as TraDo-8B (2.26x speedup, +11.2 points on AIME24). These results mark an important step toward unlocking the potential of BDLMs for test-time scaling in complex reasoning tasks.

Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive (AR) generation, yet their reliance on Transformer backbones limits inference efficiency due to quadratic attention or KV-cache overhead. We introduce DiffuMamba, a masked diffusion language model built on a bidirectional Mamba backbone that combines the diffusion objective with linear-time sequence modeling, and DiffuMamba-H, a hybrid variant with interleaved attention. Across scales up to 1.3B parameters, our models match Transformer-based diffusion in downstream performance while achieving up to 8.2x and 4.3x higher inference throughput, respectively, on long sequences. We further present a systematic analysis of inference efficiency across modern DLM variants combining asymptotic complexity with empirical measurements. Notably, cache-efficient block diffusion with Mamba mixers emerges as the only strategy that scales linearly with sequence length and achieves the strongest performance across all baselines, suggesting a promising direction for future diffusion-based generation systems.

Diffusion language models (DLMs) enable parallel, order-agnostic generation with iterative refinement, offering a flexible alternative to autoregressive large language models (LLMs). However, adapting reinforcement learning (RL) fine-tuning to DLMs remains an open challenge because of the intractable likelihood. Pioneering work such as diffu-GRPO estimated token-level likelihoods via one-step unmasking. While computationally efficient, this approach is severely biased. A more principled foundation lies in sequence-level likelihoods, where the evidence lower bound (ELBO) serves as a surrogate. Yet, despite this clean mathematical connection, ELBO-based methods have seen limited adoption due to the prohibitive cost of likelihood evaluation. In this work, we revisit ELBO estimation and disentangle its sources of variance. This decomposition motivates reducing variance through fast, deterministic integral approximations along a few pivotal dimensions. Building on this insight, we introduce Group Diffusion Policy Optimization (GDPO), a new RL algorithm tailored for DLMs. GDPO leverages simple yet effective Semi-deterministic Monte Carlo schemes to mitigate the variance explosion of ELBO estimators under vanilla double Monte Carlo sampling, yielding a provably lower-variance estimator under tight evaluation budgets. Empirically, GDPO achieves consistent gains over pretrained checkpoints and outperforms diffu-GRPO, one of the state-of-the-art baselines, on the majority of math, reasoning, and coding benchmarks.

Language models based on discrete diffusion have attracted widespread interest for their potential to provide faster generation than autoregressive models. In practice, however, they exhibit a sharp degradation of sample quality in the few-step regime, failing to realize this promise. Here we show that language models leveraging flow-based continuous denoising can outperform discrete diffusion in both quality and speed. By revisiting the fundamentals of flows over discrete modalities, we build a flow-based language model (FLM) that performs Euclidean denoising over one-hot token encodings. We show that the model can be trained by predicting the clean data via a cross entropy objective, where we introduce a simple time reparameterization that greatly improves training stability and generation quality. By distilling FLM into its associated flow map, we obtain a distilled flow map language model (FMLM) capable of few-step generation. On the LM1B and OWT language datasets, FLM attains generation quality matching state-of-the-art discrete diffusion models. With FMLM, our approach outperforms recent few-step language models across the board, with one-step generation exceeding their 8-step quality. Our work calls into question the widely held hypothesis that discrete diffusion processes are necessary for generative modeling over discrete modalities, and paves the way toward accelerated flow-based language modeling at scale. Code is available at https://github.com/david3684/flm.

Discrete diffusion language models (dLLMs) generate text by iteratively denoising a masked sequence. However, standard dLLMs condition each denoising step solely on the current hard-masked sequence, while intermediate continuous representations are discarded after sampling and remasking. We term this bottleneck the Information Island issue: continuous information remains isolated within individual denoising steps and fails to propagate across the trajectory. This bottleneck is especially harmful for reasoning, which requires intermediate reasoning state to be preserved and updated across many denoising steps. To address this limitation, we introduce MetaState, a lightweight recurrent augmentation that equips a frozen dLLM backbone with persistent, fixed-size working memory. MetaState comprises three modules with a shared time conditioner: a cross-attention Mixer that reads backbone activations into memory slots, a GRU-style Updater that integrates information across steps, and a cross-attention Injector that writes the updated memory back into the backbone. We train these modules with a dedicated K-step unrolling pipeline to learn multi-step dynamics. MetaState adds only {sim}0.6% trainable parameters while keeping the backbone frozen, and consistently improves reasoning performance over frozen baselines on mathematical reasoning and code generation benchmarks, with an average gain of 4.5% across all evaluations.

Chemical language models (CLMs) are prominent for their effectiveness in exploring chemical space and enabling molecular engineering. However, while exploring chemical-linguistic space, CLMs suffer from the gap between natural language and molecular representations. This challenge is primarily due to the inherent modeling differences between molecules and texts: molecules operate unified modeling to learn chemical space, while natural language sequentially models the semantic space. Additionally, the limited availability of high-quality text-to-molecule datasets further exacerbates this challenge. To address the problem, we first verified the information bias in molecular representations from different perspectives. We then developed the Heterogeneous Molecular Encoding (HME) framework, a unified molecular encoder compressing the molecular features from fragment sequence, topology, and conformation with Q-learning. To better model chemical-linguistic space, we further constructed the MCMoD dataset, which contains over one million molecules with various conditions, including properties, fragments, and descriptions. Experimentally, HME promotes CLMs to achieve chemical-linguistic sharing space exploration: (1) chemical space exploration with linguistic guidance, where HME achieves significant improvements (+37.8\% FCD) for molecular design in multiple constraints, even in zero-shot scenarios; (2) linguistic space exploration with molecular guidance, where HME generates textual descriptions with high qualities (+11.6\% BLEU) for molecules. These results highlight the precision of HME in handling multi-objective and cross-domain tasks, as well as its remarkable generalization capability on unseen task combinations. HME offers a new perspective on navigating chemical-linguistic sharing space, advancing the potential of CLMs in both fundamental research and practical applications in chemistry.

Generating novel active molecules for a given protein is an extremely challenging task for generative models that requires an understanding of the complex physical interactions between the molecule and its environment. In this paper, we present a novel generative model, BindGPT which uses a conceptually simple but powerful approach to create 3D molecules within the protein's binding site. Our model produces molecular graphs and conformations jointly, eliminating the need for an extra graph reconstruction step. We pretrain BindGPT on a large-scale dataset and fine-tune it with reinforcement learning using scores from external simulation software. We demonstrate how a single pretrained language model can serve at the same time as a 3D molecular generative model, conformer generator conditioned on the molecular graph, and a pocket-conditioned 3D molecule generator. Notably, the model does not make any representational equivariance assumptions about the domain of generation. We show how such simple conceptual approach combined with pretraining and scaling can perform on par or better than the current best specialized diffusion models, language models, and graph neural networks while being two orders of magnitude cheaper to sample.

Diffusion models have garnered considerable interest in the field of text generation. Several studies have explored text diffusion models with different structures and applied them to various tasks, including named entity recognition and summarization. However, there exists a notable disparity between the "easy-first" text generation process of current diffusion models and the "keyword-first" natural text generation process of humans, which has received limited attention. To bridge this gap, we propose InfoDiffusion, a non-autoregressive text diffusion model. Our approach introduces a "keyinfo-first" generation strategy and incorporates a noise schedule based on the amount of text information. In addition, InfoDiffusion combines self-conditioning with a newly proposed partially noising model structure. Experimental results show that InfoDiffusion outperforms the baseline model in terms of generation quality and diversity, as well as exhibiting higher sampling efficiency.

We discover a robust self-supervised strategy tailored towards molecular representations for generative masked language models through a series of tailored, in-depth ablations. Using this pre-training strategy, we train BARTSmiles, a BART-like model with an order of magnitude more compute than previous self-supervised molecular representations. In-depth evaluations show that BARTSmiles consistently outperforms other self-supervised representations across classification, regression, and generation tasks setting a new state-of-the-art on 11 tasks. We then quantitatively show that when applied to the molecular domain, the BART objective learns representations that implicitly encode our downstream tasks of interest. For example, by selecting seven neurons from a frozen BARTSmiles, we can obtain a model having performance within two percentage points of the full fine-tuned model on task Clintox. Lastly, we show that standard attribution interpretability methods, when applied to BARTSmiles, highlight certain substructures that chemists use to explain specific properties of molecules. The code and the pretrained model are publicly available.

Constraints are critical in text generation as LLM outputs are often unreliable when it comes to ensuring generated outputs adhere to user defined instruction or general safety guidelines. To address this gap, we present Constrained Discrete Diffusion (CDD), a novel method for enforcing constraints on natural language by integrating discrete diffusion models with differentiable optimization. Unlike conventional text generators, which often rely on post-hoc filtering or model retraining for controllable generation, we propose imposing constraints directly into the discrete diffusion sampling process. We illustrate how this technique can be applied to satisfy a variety of natural language constraints, including (i) toxicity mitigation by preventing harmful content from emerging, (ii) character and sequence level lexical constraints, and (iii) novel molecule sequence generation with specific property adherence. Experimental results show that our constraint-aware procedure achieves high fidelity in meeting these requirements while preserving fluency and semantic coherence, outperforming auto-regressive and existing discrete diffusion approaches.

Diffusion models, originally developed for image generation, have emerged as a promising alternative to autoregressive large language models (LLMs). We present a theoretical analysis comparing autoregressive and masked diffusion LLMs, revealing that the intrinsic bidirectional attention mechanism of diffusion LLMs (dLLMs) enables superior context modeling and generation controllability. However, existing dLLM applications face significant challenges in controllable generation: the native multi-step denoising process exhibits high sensitivity to sequence length, elevated hallucination rates, and prohibitive inference costs without specialized optimizations. To address these limitations, we propose Self-adaptive Schema Scaffolding (S^3), a novel framework that enables dLLMs to generate structured outputs (e.g., JSON) while maintaining semantic fidelity and accelerating inference. Our approach injects the target schema structure into the output context, reducing unnecessary computation while improving controllability. Extensive experiments demonstrate that S^3 achieves substantial improvements: 65\% increase in structural adherence, 48\% enhancement in content fidelity, and 17\% reduction in hallucination rates compared to baseline. These results establish both theoretical foundations and practical pathways for deploying diffusion models in controllable text generation tasks. Code and data will be publicly released.

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive (AR) models, offering parallel decoding and controllable sampling dynamics while achieving competitive generation quality at scale. Despite this progress, the role of sampling mechanisms in shaping refusal behavior and jailbreak robustness remains poorly understood. In this work, we present a fundamental analytical framework for step-wise refusal dynamics, enabling comparison between AR and diffusion sampling. Our analysis reveals that the sampling strategy itself plays a central role in safety behavior, as a factor distinct from the underlying learned representations. Motivated by this analysis, we introduce the Step-Wise Refusal Internal Dynamics (SRI) signal, which supports interpretability and improved safety for both AR and DLMs. We demonstrate that the geometric structure of SRI captures internal recovery dynamics, and identifies anomalous behavior in harmful generations as cases of incomplete internal recovery that are not observable at the text level. This structure enables lightweight inference-time detectors that generalize to unseen attacks while matching or outperforming existing defenses with over 100times lower inference overhead.

Diffusion language models offer parallel token generation and inherent bidirectionality, promising more efficient and powerful sequence modeling compared to autoregressive approaches. However, state-of-the-art diffusion models (e.g., Dream 7B, LLaDA 8B) suffer from slow inference. While they match the quality of similarly sized Autoregressive (AR) Models (e.g., Qwen2.5 7B, Llama3 8B), their iterative denoising requires multiple full-sequence forward passes, resulting in high computational costs and latency, particularly for long input prompts and long-context scenarios. Furthermore, parallel token generation introduces token incoherence problems, and current sampling heuristics suffer from significant quality drops with decreasing denoising steps. We address these limitations with two training-free techniques. First, we propose FreeCache, a Key-Value (KV) approximation caching technique that reuses stable KV projections across denoising steps, effectively reducing the computational cost of DLM inference. Second, we introduce Guided Diffusion, a training-free method that uses a lightweight pretrained autoregressive model to supervise token unmasking, dramatically reducing the total number of denoising iterations without sacrificing quality. We conduct extensive evaluations on open-source reasoning benchmarks, and our combined methods deliver up to a 34x end-to-end speedup without compromising accuracy. For the first time, diffusion language models achieve a comparable and even faster latency as the widely adopted autoregressive models. Our work successfully paved the way for scaling up the diffusion language model to a broader scope of applications across different domains.

Diffusion models have emerged as a promising approach for text generation, with recent works falling into two main categories: discrete and continuous diffusion models. Discrete diffusion models apply token corruption independently using categorical distributions, allowing for different diffusion progress across tokens but lacking fine-grained control. Continuous diffusion models map tokens to continuous spaces and apply fine-grained noise, but the diffusion progress is uniform across tokens, limiting their ability to capture semantic nuances. To address these limitations, we propose \underline{N}on-simultan\underline{e}ous C\underline{o}ntinuous \underline{Diff}usion Models (NeoDiff), a novel diffusion model that integrates the strengths of both discrete and continuous approaches. NeoDiff introduces a Poisson diffusion process for the forward process, enabling a flexible and fine-grained noising paradigm, and employs a time predictor for the reverse process to adaptively modulate the denoising progress based on token semantics. Furthermore, NeoDiff utilizes an optimized schedule for inference to ensure more precise noise control and improved performance. Our approach unifies the theories of discrete and continuous diffusion models, offering a more principled and effective framework for text generation. Experimental results on several text generation tasks demonstrate NeoDiff's superior performance compared to baselines of non-autoregressive continuous and discrete diffusion models, iterative-based methods and autoregressive diffusion-based methods. These results highlight NeoDiff's potential as a powerful tool for generating high-quality text and advancing the field of diffusion-based text generation.

Diffusion Language Models (DLMs) offer a promising alternative for language modeling by enabling parallel decoding through iterative refinement. However, most DLMs rely on hard binary masking and discrete token assignments, which hinder the revision of early decisions and underutilize intermediate probabilistic representations. In this paper, we propose EvoToken-DLM, a novel diffusion-based language modeling approach that replaces hard binary masks with evolving soft token distributions. EvoToken-DLM enables a progressive transition from masked states to discrete outputs, supporting revisable decoding. To effectively support this evolution, we introduce continuous trajectory supervision, which aligns training objectives with iterative probabilistic updates. Extensive experiments across multiple benchmarks show that EvoToken-DLM consistently achieves superior performance, outperforming strong diffusion-based and masked DLM baselines. Project webpage: https://aim-uofa.github.io/EvoTokenDLM.

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language generation, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github: https://github.com/YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy.

Masked Diffusion Language Models (MDLMs) have emerged as a compelling non-autoregressive alternative to standard large language models; however, their application to morphologically rich languages remains limited. In this paper, we introduce Diffutron, a masked diffusion language model specifically designed for Turkish. Our approach leverages a resource-efficient training pipeline, starting with LoRA-based continual pre-training of a multilingual encoder on a large-scale corpus. To enable generative capabilities, we employ a progressive instruction-tuning strategy, sequentially adapting the model on general and task-specific instruction sets. Experimental results across comprehensive benchmarks demonstrate that, despite its compact size, our model achieves competitive performance compared to existing multi-billion-parameter baselines. These findings validate the effectiveness of masked diffusion modeling combined with multi-stage tuning for non-autoregressive text generation in Turkish.

Diffusion language models enable any-order generation and bidirectional conditioning, offering appealing flexibility for tasks such as infilling, rewriting, and self-correction. However, their formulation-predicting one part of a sequence from another within a single-step dependency-limits modeling depth and often yields lower sample quality and stability than autoregressive (AR) models. To address this, we revisit autoregressive modeling as a foundation and reformulate diffusion-style training into a structured multi-group prediction process. We propose Any-order Any-subset Autoregressive modeling (A3), a generalized framework that extends the standard AR factorization to arbitrary token groups and generation orders. A3 preserves the probabilistic rigor and multi-layer dependency modeling of AR while inheriting diffusion models' flexibility for parallel and bidirectional generation. We implement A3 through a two-stream attention architecture and a progressive adaptation strategy that transitions pretrained AR models toward any-order prediction. Experiments on question answering, commonsense reasoning, and story infilling demonstrate that A3 outperforms diffusion-based models while maintaining flexible decoding. This work offers a unified approach for a flexible, efficient, and novel language modeling paradigm.

Diffusion Language Models (DLMs) promise parallel generation and bidirectional context, yet they underperform autoregressive (AR) models in both likelihood modeling and generated text quality. We identify that this performance gap arises when important tokens (e.g., key words or low-frequency words that anchor a sentence) are masked early in the forward process, limiting contextual information for accurate reconstruction. To address this, we introduce the Anchored Diffusion Language Model (ADLM), a novel two-stage framework that first predicts distributions over important tokens via an anchor network, and then predicts the likelihoods of missing tokens conditioned on the anchored predictions. ADLM significantly improves test perplexity on LM1B and OpenWebText, achieving up to 25.4% gains over prior DLMs, and narrows the gap with strong AR baselines. It also achieves state-of-the-art performance in zero-shot generalization across seven benchmarks and surpasses AR models in MAUVE score, which marks the first time a DLM generates better human-like text than an AR model. Theoretically, we derive an Anchored Negative Evidence Lower Bound (ANELBO) objective and show that anchoring improves sample complexity and likelihood modeling. Beyond diffusion, anchoring boosts performance in AR models and enhances reasoning in math and logic tasks, outperforming existing chain-of-thought approaches

In this work, we introduce ChemBFN, a language model that handles chemistry tasks based on Bayesian flow networks working on discrete data. A new accuracy schedule is proposed to improve the sampling quality by significantly reducing the reconstruction loss. We show evidence that our method is appropriate for generating molecules with satisfied diversity even when a smaller number of sampling steps is used. A classifier-free guidance method is adapted for conditional generation. It is also worthwhile to point out that after generative training, our model can be fine-tuned on regression and classification tasks with the state-of-the-art performance, which opens the gate of building all-in-one models in a single module style. Our model has been open sourced at https://github.com/Augus1999/bayesian-flow-network-for-chemistry.

Although diffusion language models (DLMs) are evolving quickly, many recent models converge on a set of shared components. These components, however, are distributed across ad-hoc research codebases or lack transparent implementations, making them difficult to reproduce or extend. As the field accelerates, there is a clear need for a unified framework that standardizes these common components while remaining flexible enough to support new methods and architectures. To address this gap, we introduce dLLM, an open-source framework that unifies the core components of diffusion language modeling -- training, inference, and evaluation -- and makes them easy to customize for new designs. With dLLM, users can reproduce, finetune, deploy, and evaluate open-source large DLMs such as LLaDA and Dream through a standardized pipeline. The framework also provides minimal, reproducible recipes for building small DLMs from scratch with accessible compute, including converting any BERT-style encoder or autoregressive LM into a DLM. We also release the checkpoints of these small DLMs to make DLMs more accessible and accelerate future research.

Despite the remarkable strides made by autoregressive language models, their potential is often hampered by the slow inference speeds inherent in sequential token generation. Blockwise parallel decoding (BPD) was proposed by Stern et al. (2018) as a way to improve inference speed of language models. In this paper, we make two contributions to understanding and improving BPD drafts. We first offer an analysis of the token distributions produced by the BPD prediction heads. Secondly, we use this analysis to inform algorithms to improve BPD inference speed by refining the BPD drafts using small n-gram or neural language models. We empirically show that these refined BPD drafts yield a higher average verified prefix length across tasks.

Autoregressive (AR) Large Language Models (LLMs) have demonstrated significant success across numerous tasks. However, the AR modeling paradigm presents certain limitations; for instance, contemporary autoregressive LLMs are trained to generate one token at a time, which can result in noticeable latency. Recent advances have indicated that search and repeated sampling can enhance performance in various applications, such as theorem proving, code generation, and alignment, by utilizing greater computational resources during inference. In this study, we demonstrate that diffusion language models are capable of generating at least 32 tokens simultaneously, while exceeding the performance of AR models in text quality and on the LAMBADA natural language understanding benchmark. This outcome is achieved through a novel distillation method for discrete diffusion models, which reduces the number of inference steps by a factor of 32-64. Practically, our models, even without caching, can generate tokens at a rate that is up to 8 times faster than AR models employing KV caching, and we anticipate further improvements with the inclusion of caching. Moreover, we demonstrate the efficacy of our approach for diffusion language models with up to 860M parameters.

The diffusion model has been proven a powerful generative model in recent years, yet remains a challenge in generating visual text. Several methods alleviated this issue by incorporating explicit text position and content as guidance on where and what text to render. However, these methods still suffer from several drawbacks, such as limited flexibility and automation, constrained capability of layout prediction, and restricted style diversity. In this paper, we present TextDiffuser-2, aiming to unleash the power of language models for text rendering. Firstly, we fine-tune a large language model for layout planning. The large language model is capable of automatically generating keywords for text rendering and also supports layout modification through chatting. Secondly, we utilize the language model within the diffusion model to encode the position and texts at the line level. Unlike previous methods that employed tight character-level guidance, this approach generates more diverse text images. We conduct extensive experiments and incorporate user studies involving human participants as well as GPT-4V, validating TextDiffuser-2's capacity to achieve a more rational text layout and generation with enhanced diversity. The code and model will be available at https://aka.ms/textdiffuser-2.

Diffusion language models (DLMs) generate text through iterative denoising, but inference requires full-sequence attention at every iteration, resulting in substantial redundant computation on masked tokens. Block-wise diffusion can reduce this cost, yet it typically relies on retraining and constrained update orders, limiting its direct applicability to pretrained DLMs. Our token-level analysis reveals pronounced structural locality in DLM inference. Decoding is driven by a small set of prefix-localized active tokens; the influence of distant undecoded context diminishes rapidly, and decoded tokens exhibit stage-wise temporal stability, enabling reuse of intermediate representations except for a brief post-decode transient. Motivated by these observations, we propose \placeholderThe source code is available at https://github.com/vhicrgit/Window-Diffusion., a window-based token pruning and caching method for inference. We maintain a local computation window that slides rightward as denoising progresses, and partition undecoded tokens into: (i) active tokens that are computed online, (ii) buffer tokens whose KV states are cached and periodically refreshed, and (iii) far-field tokens that are pruned outside the window. Computation is restricted to active and buffer tokens within the window, while far-field tokens are omitted at each stage. Experiments on LLaDA and Dream show that, under matched compute budgets, our method achieves up to 99times inference speedup while largely preserving generation performance.

Generative tasks about molecules, including but not limited to molecule generation, are crucial for drug discovery and material design, and have consistently attracted significant attention. In recent years, diffusion models have emerged as an impressive class of deep generative models, sparking extensive research and leading to numerous studies on their application to molecular generative tasks. Despite the proliferation of related work, there remains a notable lack of up-to-date and systematic surveys in this area. Particularly, due to the diversity of diffusion model formulations, molecular data modalities, and generative task types, the research landscape is challenging to navigate, hindering understanding and limiting the area's growth. To address this, this paper conducts a comprehensive survey of diffusion model-based molecular generative methods. We systematically review the research from the perspectives of methodological formulations, data modalities, and task types, offering a novel taxonomy. This survey aims to facilitate understanding and further flourishing development in this area. The relevant papers are summarized at: https://github.com/AzureLeon1/awesome-molecular-diffusion-models.

Diffusion Language Models (DLMs) are often advertised as enabling parallel token generation, yet practical fast DLMs frequently converge to left-to-right, autoregressive (AR)-like decoding dynamics. In contrast, genuinely non-AR generation is promising because it removes AR's sequential bottleneck, better exploiting parallel hardware to reduce synchronization/communication overhead and improve latency scaling with output length. We argue that a primary driver of AR-like decoding is a mismatch between DLM objectives and the highly sequential structure of widely used training data, including standard pretraining corpora and long chain-of-thought (CoT) supervision. Motivated by this diagnosis, we propose NAP (Non-Autoregressive Parallel DLMs), a proof-of-concept, data-centric approach that better aligns supervision with non-AR parallel decoding. NAP curates examples as multiple independent reasoning trajectories and couples them with a parallel-forced decoding strategy that encourages multi-token parallel updates. Across math reasoning benchmarks, NAP yields stronger performance under parallel decoding than DLMs trained on standard long CoT data, with gains growing as parallelism increases. Our results suggest that revisiting data and supervision is a principled direction for mitigating AR-like behavior and moving toward genuinely non-autoregressive parallel generation in DLMs. Our code is available at https://github.com/pixeli99/NAP.

Uniform-state discrete diffusion models excel at few-step generation and guidance due to their ability to self-correct, making them preferred over autoregressive or Masked diffusion models in these settings. However, their sampling quality plateaus with ancestral samplers as the number of steps increases. We introduce a family of Predictor-Corrector (PC) samplers for discrete diffusion that generalize prior methods and apply to arbitrary noise processes. When paired with uniform-state diffusion, our samplers outperform ancestral sampling on both language and image modeling, achieving lower generative perplexity at matched unigram entropy on OpenWebText and better FID/IS scores on CIFAR10. Crucially, unlike conventional samplers, our PC methods continue to improve with more sampling steps. Taken together, these findings call into question the assumption that Masked diffusion is the inevitable future of diffusion-based language modeling. Beyond sampling, we develop a memory-efficient curriculum for the Gaussian relaxation training phase, reducing training time by 25% and memory by 33% compared to Duo while maintaining comparable perplexity on OpenWebText and LM1B and strong downstream performance. We release code, checkpoints, and a video-tutorial on: https://s-sahoo.com/duo-ch2

Diffusion models have gained prominence in generating high-quality sequences of text. Nevertheless, current approaches predominantly represent discrete text within a continuous diffusion space, which incurs substantial computational overhead during training and results in slower sampling speeds. In this paper, we introduce a soft absorbing state that facilitates the diffusion model in learning to reconstruct discrete mutations based on the underlying Gaussian space, thereby enhancing its capacity to recover conditional signals. During the sampling phase, we employ state-of-the-art ODE solvers within the continuous space to expedite the sampling process. Comprehensive experimental evaluations reveal that our proposed method effectively accelerates the training convergence by 4x and generates samples of similar quality 800x faster, rendering it significantly closer to practical application. The code is released at \url{https://github.com/Shark-NLP/DiffuSeq

Masked (or absorbing) diffusion is actively explored as an alternative to autoregressive models for generative modeling of discrete data. However, existing work in this area has been hindered by unnecessarily complex model formulations and unclear relationships between different perspectives, leading to suboptimal parameterization, training objectives, and ad hoc adjustments to counteract these issues. In this work, we aim to provide a simple and general framework that unlocks the full potential of masked diffusion models. We show that the continuous-time variational objective of masked diffusion models is a simple weighted integral of cross-entropy losses. Our framework also enables training generalized masked diffusion models with state-dependent masking schedules. When evaluated by perplexity, our models trained on OpenWebText surpass prior diffusion language models at GPT-2 scale and demonstrate superior performance on 4 out of 5 zero-shot language modeling tasks. Furthermore, our models vastly outperform previous discrete diffusion models on pixel-level image modeling, achieving 2.78~(CIFAR-10) and 3.42 (ImageNet 64times64) bits per dimension that are comparable or better than autoregressive models of similar sizes.

Diffusion Language Models (DLMs) have been seen as a promising competitor for autoregressive language models. However, diffusion language models have long been constrained by slow inference. A core challenge is that their non-autoregressive architecture and bidirectional attention preclude the key-value cache that accelerates decoding. We address this bottleneck by proposing a KV-cache-like mechanism, delayed KV-Cache, for the denoising process of DLMs. Our approach is motivated by the observation that different tokens have distinct representation dynamics throughout the diffusion process. Accordingly, we propose a delayed and conditioned caching strategy for key and value states. We design two complementary variants to cache key and value step-by-step: (1) dKV-Cache-Decode, which provides almost lossless acceleration, and even improves performance on long sequences, suggesting that existing DLMs may under-utilise contextual information during inference. (2) dKV-Cache-Greedy, which has aggressive caching with reduced lifespan, achieving higher speed-ups with quadratic time complexity at the cost of some performance degradation. dKV-Cache, in final, achieves from 2-10x speedup in inference, largely narrowing the gap between ARs and DLMs. We evaluate our dKV-Cache on several benchmarks, delivering acceleration across general language understanding, mathematical, and code-generation benchmarks. Experiments demonstrate that cache can also be used in DLMs, even in a training-free manner from current DLMs.

Diffusion Language Models (DLMs) offer a promising parallel generation paradigm but suffer from slow inference due to numerous refinement steps and the inability to use standard KV caching. We introduce CDLM (Consistency Diffusion Language Models), a training-based acceleration method that simultaneously tackles both bottlenecks. CDLM integrates consistency modeling to drastically reduce the number of required sampling steps by enabling multi-token finalization. Furthermore, we enforce a block-wise causal attention mask during fine-tuning, making the model fully compatible with KV caching. Experiments show CDLM achieves 3.6x-14.5x lower latency while maintaining competitive accuracy on math and coding tasks. The full training and evaluation code is available at https://github.com/SqueezeAILab/CDLM.

Autoregressive (AR) large language models (LLMs) have achieved remarkable performance across a wide range of natural language tasks, yet their inherent sequential decoding limits inference efficiency. In this work, we propose Fast-dLLM v2, a carefully designed block diffusion language model (dLLM) that efficiently adapts pretrained AR models into dLLMs for parallel text generation, requiring only approximately 1B tokens of fine-tuning. This represents a 500x reduction in training data compared to full-attention diffusion LLMs such as Dream (580B tokens), while preserving the original model's performance. Our approach introduces a novel training recipe that combines a block diffusion mechanism with a complementary attention mask, enabling blockwise bidirectional context modeling without sacrificing AR training objectives. To further accelerate decoding, we design a hierarchical caching mechanism: a block-level cache that stores historical context representations across blocks, and a sub-block cache that enables efficient parallel generation within partially decoded blocks. Coupled with our parallel decoding pipeline, Fast-dLLM v2 achieves up to 2.5x speedup over standard AR decoding without compromising generation quality. Extensive experiments across diverse benchmarks demonstrate that Fast-dLLM v2 matches or surpasses AR baselines in accuracy, while delivering state-of-the-art efficiency among dLLMs - marking a significant step toward the practical deployment of fast and accurate LLMs. Code and model will be publicly released.

Molecular property prediction has gained significant attention due to its transformative potential in multiple scientific disciplines. Conventionally, a molecule graph can be represented either as a graph-structured data or a SMILES text. Recently, the rapid development of Large Language Models (LLMs) has revolutionized the field of NLP. Although it is natural to utilize LLMs to assist in understanding molecules represented by SMILES, the exploration of how LLMs will impact molecular property prediction is still in its early stage. In this work, we advance towards this objective through two perspectives: zero/few-shot molecular classification, and using the new explanations generated by LLMs as representations of molecules. To be specific, we first prompt LLMs to do in-context molecular classification and evaluate their performance. After that, we employ LLMs to generate semantically enriched explanations for the original SMILES and then leverage that to fine-tune a small-scale LM model for multiple downstream tasks. The experimental results highlight the superiority of text explanations as molecular representations across multiple benchmark datasets, and confirm the immense potential of LLMs in molecular property prediction tasks. Codes are available at https://github.com/ChnQ/LLM4Mol.

Diffusion language models (DLMs) provide a bidirectional generation framework naturally suited for infilling, yet their performance is constrained by the pre-specified infilling length. In this paper, we reveal that DLMs possess an inherent ability to discover the correct infilling length. We identify two key statistical phenomena in the first-step denoising confidence: a local Oracle Peak that emerges near the ground-truth length and a systematic Length Bias that often obscures this signal. By leveraging this signal and calibrating the bias, our training-free method CAL (Calibrated Adaptive Length) enables DLMs to approximate the optimal length through an efficient search before formal decoding. Empirical evaluations demonstrate that CAL improves Pass@1 by up to 47.7\% over fixed-length baselines and 40.5\% over chat-based adaptive methods in code infilling, while boosting BLEU-2 and ROUGE-L by up to 8.5\% and 9.9\% in text infilling. These results demonstrate that CAL paves the way for robust DLM infilling without requiring any specialized training. Code is available at https://github.com/NiuHechang/Calibrated_Adaptive_Length.

This paper introduces diffusion protein language model (DPLM), a versatile protein language model that demonstrates strong generative and predictive capabilities for protein sequences. We first pre-train scalable DPLMs from evolutionary-scale protein sequences within a generative self-supervised discrete diffusion probabilistic framework, which generalizes language modeling for proteins in a principled way. After pre-training, DPLM exhibits the ability to generate structurally plausible, novel, and diverse protein sequences for unconditional generation. We further demonstrate the proposed diffusion generative pre-training makes DPLM possess a better understanding of proteins, making it a superior representation learner, which can be fine-tuned for various predictive tasks, comparing favorably to ESM2 (Lin et al., 2022). Moreover, DPLM can be tailored for various needs, which showcases its prowess of conditional generation in several ways: (1) conditioning on partial peptide sequences, e.g., generating scaffolds for functional motifs with high success rate; (2) incorporating other modalities as conditioner, e.g., structure-conditioned generation for inverse folding; and (3) steering sequence generation towards desired properties, e.g., satisfying specified secondary structures, through a plug-and-play classifier guidance. Code is released at https://github.com/bytedance/dplm.

Diffusion Large Language Models (dLLMs) have demonstrated promising generative capabilities and are increasingly used to produce formal languages defined by context-free grammars, such as source code and chemical expressions. However, as probabilistic models, they still struggle to generate syntactically valid outputs reliably. A natural and promising direction to address this issue is to adapt constrained decoding techniques to enforce grammatical correctness during generation. However, applying these techniques faces two primary obstacles. On the one hand, the non-autoregressive nature of dLLMs renders most existing constrained decoding approaches inapplicable. On the other hand, current approaches specifically designed for dLLMs may allow intermediate outputs that are impossible to complete into valid sentences, which significantly limits their reliability in practice. To address these challenges, we present LAVE, a constrained decoding approach specifically designed for dLLMs. Our approach leverages a key property of dLLMs, namely their ability to predict token distributions for all positions in parallel during each forward pass. Whenever a new token is proposed by model, LAVE performs lookahead using these distributions to efficiently and reliably verify the validity of the proposed token. This design ensures reliable constraints by reliably preserving the potential for intermediate outputs to be extended into valid sentences. Extensive experiments across four widely used dLLMs and three representative benchmarks demonstrate that LAVE consistently outperforms existing baselines and achieves substantial improvements in syntactic correctness, while incurring negligible runtime overhead.

Molecules play a crucial role in biomedical research and discovery, particularly in the field of small molecule drug development. Given the rapid advancements in large language models, especially the recent emergence of reasoning models, it is natural to explore how a general-purpose language model can be efficiently adapted for molecular science applications. In this work, we introduce BioMedGPT-Mol, a molecular language model designed to support molecular understanding and generation tasks. By curating and unifying existing public instruction datasets, we have assembled a large-scale, comprehensive, and high-quality training dataset. The model is then fine-tuned through a meticulously designed multi-task learning framework. On a consolidated benchmark derived from LlaSMol, TOMG-Bench, and MuMOInstruct, BioMedGPT-Mol achieves remarkable performance. Our experimental results demonstrate that a general-purpose reasoning model can be effectively and efficiently post-trained into a professional molecular language model through a well-structured multi-task curriculum. Leveraging these capabilities, we further apply the model to multi-step retrosynthetic planning, achieving state-of-the-art performance on RetroBench and demonstrating its superior efficacy as an end-to-end retrosynthetic planner. We anticipate that our approach can be extended to other biomedical scientific domains.

Large Language Models(LLMs) have demonstrated remarkable performance across various domains, yet their capabilities in molecular reasoning remain insufficiently explored. Current approaches tend to rely heavily on general-purpose prompting, which lacks domain-specific molecular semantics, while those that use fine-tuning strategies often face challenges with interpretability and reasoning depth. To address these issues, we introduce MolReasoner, a two-stage framework designed to transition LLMs from memorization towards chemical reasoning. First, we propose Mol-SFT, which initializes the model's reasoning abilities via synthetic Chain-of-Thought(CoT) samples generated by GPT-4o and verified for chemical accuracy. Subsequently, Mol-RL applies reinforcement learning with specialized reward functions designed explicitly to align chemical structures with linguistic descriptions, thereby enhancing molecular reasoning capabilities. Our approach notably enhances interpretability, improving the model 's molecular understanding and enabling better generalization. Extensive experiments demonstrate that MolReasoner outperforms existing methods, and marking a significant shift from memorization-based outputs to robust chemical reasoning.

Chemical Language Models (CLMs) pre-trained on large scale molecular data are widely used for molecular property prediction. However, the common belief that increasing training resources such as model size, dataset size, and training compute improves both pretraining loss and downstream task performance has not been systematically validated in the chemical domain. In this work, we evaluate this assumption by pretraining CLMs while scaling training resources and measuring transfer performance across diverse molecular property prediction (MPP) tasks. We find that while pretraining loss consistently decreases with increased training resources, downstream task performance shows limited improvement. Moreover, alternative metrics based on the Hessian or loss landscape also fail to estimate downstream performance in CLMs. We further identify conditions under which downstream performance saturates or degrades despite continued improvements in pretraining metrics, and analyze the underlying task dependent failure modes through parameter space visualizations. These results expose a gap between pretraining based evaluation and downstream performance, and emphasize the need for model selection and evaluation strategies that explicitly account for downstream task characteristics.

Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval. Empirically, RADD is up to 3.5 times faster while achieving similar performance with the strongest baseline. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at https://github.com/ML-GSAI/RADD.

Language Models (LMs) have greatly influenced diverse domains. However, their inherent limitation in comprehending 3D molecular structures has considerably constrained their potential in the biomolecular domain. To bridge this gap, we focus on 3D molecule-text interpretation, and propose 3D-MoLM: 3D-Molecular Language Modeling. Specifically, 3D-MoLM enables an LM to interpret and analyze 3D molecules by equipping the LM with a 3D molecular encoder. This integration is achieved by a 3D molecule-text projector, bridging the 3D molecular encoder's representation space and the LM's input space. Moreover, to enhance 3D-MoLM's ability of cross-modal molecular understanding and instruction following, we meticulously curated a 3D molecule-centric instruction tuning dataset -- 3D-MoIT. Through 3D molecule-text alignment and 3D molecule-centric instruction tuning, 3D-MoLM establishes an integration of 3D molecular encoder and LM. It significantly surpasses existing baselines on downstream tasks, including molecule-text retrieval, molecule captioning, and more challenging open-text molecular QA tasks, especially focusing on 3D-dependent properties.

While various models and computational tools have been proposed for structure and property analysis of molecules, generating molecules that conform to all desired structures and properties remains a challenge. Here, we introduce a multi-constraint molecular generation large language model, TSMMG, which, akin to a student, incorporates knowledge from various small models and tools, namely, the 'teachers'. To train TSMMG, we construct a large set of text-molecule pairs by extracting molecular knowledge from these 'teachers', enabling it to generate novel molecules that conform to the descriptions through various text prompts. We experimentally show that TSMMG remarkably performs in generating molecules meeting complex, natural language-described property requirements across two-, three-, and four-constraint tasks, with an average molecular validity of over 99% and success ratio of 82.58%, 68.03%, and 67.48%, respectively. The model also exhibits adaptability through zero-shot testing, creating molecules that satisfy combinations of properties that have not been encountered. It can comprehend text inputs with various language styles, extending beyond the confines of outlined prompts, as confirmed through empirical validation. Additionally, the knowledge distillation feature of TSMMG contributes to the continuous enhancement of small models, while the innovative approach to dataset construction effectively addresses the issues of data scarcity and quality, which positions TSMMG as a promising tool in the domains of drug discovery and materials science.

In recent years, Large Language Models (LLMs) have achieved significant success in natural language processing (NLP) and various interdisciplinary areas. However, applying LLMs to chemistry is a complex task that requires specialized domain knowledge. This paper provides a thorough exploration of the nuanced methodologies employed in integrating LLMs into the field of chemistry, delving into the complexities and innovations at this interdisciplinary juncture. Specifically, our analysis begins with examining how molecular information is fed into LLMs through various representation and tokenization methods. We then categorize chemical LLMs into three distinct groups based on the domain and modality of their input data, and discuss approaches for integrating these inputs for LLMs. Furthermore, this paper delves into the pretraining objectives with adaptations to chemical LLMs. After that, we explore the diverse applications of LLMs in chemistry, including novel paradigms for their application in chemistry tasks. Finally, we identify promising research directions, including further integration with chemical knowledge, advancements in continual learning, and improvements in model interpretability, paving the way for groundbreaking developments in the field.

Masked diffusion models (MDMs) are a potential alternative to autoregressive models (ARMs) for language generation, but generation quality depends critically on the generation order. Prior work either hard-codes an ordering (e.g., blockwise left-to-right) or learns an ordering policy for a pretrained MDM, which incurs extra cost and can yield suboptimal solutions due to the two-stage optimization. Motivated by this, we propose order-expressive masked diffusion model (OeMDM) for a broad class of diffusion generative processes with various generation orders, enabling the interpretation of MDM, ARM, and block diffusion in a single framework. Furthermore, building on OeMDM, we introduce learnable-order masked diffusion model (LoMDM), which jointly learns the generation ordering and diffusion backbone through a single objective from scratch, enabling the diffusion model to generate text in context-dependent ordering. Empirically, we confirm that LoMDM outperforms various discrete diffusion models across multiple language modeling benchmarks.

Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have some limitations in modeling discrete data, e.g., languages. For example, the generally used Gaussian noise can not handle the discrete corruption well, and the objectives in continuous spaces fail to be stable for textual data in the diffusion process especially when the dimension is high. To alleviate these issues, we introduce a novel diffusion model for language modeling, Masked-Diffuse LM, with lower training cost and better performances, inspired by linguistic features in languages. Specifically, we design a linguistic-informed forward process which adds corruptions to the text through strategically soft-masking to better noise the textual data. Also, we directly predict the categorical distribution with cross-entropy loss function in every diffusion step to connect the continuous space and discrete space in a more efficient and straightforward way. Through experiments on 5 controlled generation tasks, we demonstrate that our Masked-Diffuse LM can achieve better generation quality than the state-of-the-art diffusion models with better efficiency.

Recent byte-level language models (LMs) match the performance of token-level models without relying on subword vocabularies, yet their utility is limited by slow, byte-by-byte autoregressive generation. We address this bottleneck in the Byte Latent Transformer (BLT) through new training and generation techniques. First, we introduce BLT Diffusion (BLT-D), a new model and our fastest BLT variant, trained with an auxiliary block-wise diffusion objective alongside the standard next-byte prediction loss. This enables an inference procedure that generates multiple bytes in parallel per decoding step, substantially reducing the number of forward passes required to generate a sequence. Second, we propose two extensions inspired by speculative decoding that trade some of this speed for higher generation quality: BLT Self-speculation (BLT-S), in which BLT's local decoder continues generating past its normal patch boundaries to draft bytes, which are then verified with a single full-model forward pass; and BLT Diffusion+Verification (BLT-DV), which augments BLT-D with an autoregressive verification step after diffusion-based generation. All methods may achieve an estimated memory-bandwidth cost over 50% lower than BLT on generation tasks. Each approach offers its own unique advantages, together removing key barriers to the practical use of byte-level LMs.

We present significant extensions to diffusion-based sequence generation models, blurring the line with autoregressive language models. We introduce hyperschedules, which assign distinct noise schedules to individual token positions, generalizing both autoregressive models (e.g., GPT) and conventional diffusion models (e.g., SEDD, MDLM) as special cases. Second, we propose two hybrid token-wise noising processes that interpolate between absorbing and uniform processes, enabling the model to fix past mistakes, and we introduce a novel inference algorithm that leverages this new feature in a simplified context inspired from MDLM. To support efficient training and inference, we design attention masks compatible with KV-caching. Our methods achieve state-of-the-art perplexity and generate diverse, high-quality sequences across standard benchmarks, suggesting a promising path for autoregressive diffusion-based sequence generation.

Graph generation has been dominated by autoregressive models due to their simplicity and effectiveness, despite their sensitivity to ordering. Yet diffusion models have garnered increasing attention, as they offer comparable performance while being permutation-invariant. Current graph diffusion models generate graphs in a one-shot fashion, but they require extra features and thousands of denoising steps to achieve optimal performance. We introduce PARD, a Permutation-invariant Auto Regressive Diffusion model that integrates diffusion models with autoregressive methods. PARD harnesses the effectiveness and efficiency of the autoregressive model while maintaining permutation invariance without ordering sensitivity. Specifically, we show that contrary to sets, elements in a graph are not entirely unordered and there is a unique partial order for nodes and edges. With this partial order, PARD generates a graph in a block-by-block, autoregressive fashion, where each block's probability is conditionally modeled by a shared diffusion model with an equivariant network. To ensure efficiency while being expressive, we further propose a higher-order graph transformer, which integrates transformer with PPGN. Like GPT, we extend the higher-order graph transformer to support parallel training of all blocks. Without any extra features, PARD achieves state-of-the-art performance on molecular and non-molecular datasets, and scales to large datasets like MOSES containing 1.9M molecules.

Despite the growing success of diffusion models in continuous-valued domains (e.g., images), similar efforts for discrete domains such as text have yet to match the performance of autoregressive language models. In this work, we present SSD-LM -- a diffusion-based language model with two key design choices. First, SSD-LM is semi-autoregressive, iteratively generating blocks of text, allowing for flexible output length at decoding time while enabling local bidirectional context updates. Second, it is simplex-based, performing diffusion on the natural vocabulary space rather than a learned latent space, allowing us to incorporate classifier guidance and modular control using off-the-shelf classifiers without any adaptation. We evaluate SSD-LM on unconstrained text generation benchmarks, and show that it matches or outperforms strong autoregressive GPT-2 models across standard quality and diversity metrics, while vastly outperforming diffusion-based baselines. On controlled text generation, SSD-LM also outperforms competitive baselines, with an extra advantage in modularity.

Machine learning, notably deep learning, has significantly propelled molecular investigations within the biochemical sphere. Traditionally, modeling for such research has centered around a handful of paradigms. For instance, the prediction paradigm is frequently deployed for tasks such as molecular property prediction. To enhance the generation and decipherability of purely data-driven models, scholars have integrated biochemical domain knowledge into these molecular study models. This integration has sparked a surge in paradigm transfer, which is solving one molecular learning task by reformulating it as another one. With the emergence of Large Language Models, these paradigms have demonstrated an escalating trend towards harmonized unification. In this work, we delineate a literature survey focused on knowledge-informed molecular learning from the perspective of paradigm transfer. We classify the paradigms, scrutinize their methodologies, and dissect the contribution of domain knowledge. Moreover, we encapsulate prevailing trends and identify intriguing avenues for future exploration in molecular learning.

We consider molecule generation in 3D space using language models (LMs), which requires discrete tokenization of 3D molecular geometries. Although tokenization of molecular graphs exists, that for 3D geometries is largely unexplored. Here, we attempt to bridge this gap by proposing the Geo2Seq, which converts molecular geometries into SE(3)-invariant 1D discrete sequences. Geo2Seq consists of canonical labeling and invariant spherical representation steps, which together maintain geometric and atomic fidelity in a format conducive to LMs. Our experiments show that, when coupled with Geo2Seq, various LMs excel in molecular geometry generation, especially in controlled generation tasks.

Auto-regressive Large Language Models (LLMs) achieve strong performance on coding tasks, but incur high memory and inference costs. Diffusion-based language models (d-LLMs) offer bounded inference cost via iterative denoising, but their behavior under post-training quantization (PTQ) has been sparsely explored. We investigate the application and robustness of PTQ techniques, specifically GPTQ and a modified Hessian-Aware Quantization (HAWQ) algorithm, on a diffusion-based coding LLM (CoDA) and observe that these methods applied to CoDA exhibit greater robustness at low bitwidths compared to Qwen3-1.7B, its auto-regressive counterpart, under a standardized evaluation pipeline. We find that in our setup, CoDA exhibits greater robustness at low bitwidths (2-4 bits), with smaller accuracy degradation across HumanEval and MBPP benchmarks. Additionally, mixed-precision configurations derived from HAWQ provide smooth trade-offs across accuracy, latency, and memory. The results suggest that diffusion LLMs may offer advantages for efficient deployment due to more quantization-resilience.

Diffusion Language Models (DLMs) have emerged as a compelling alternative to autoregressive approaches, enabling parallel text generation with competitive performance. Despite these advantages, there is a critical instability in DLMs: the moving sink phenomenon. Our analysis indicates that sink tokens exhibit low-norm representations in the Transformer's value space, and that the moving sink phenomenon serves as a protective mechanism in DLMs to prevent excessive information mixing. However, their unpredictable positions across diffusion steps undermine inference robustness. To resolve this, we propose a simple but effective extra sink token implemented via a modified attention mask. Specifically, we introduce a special token constrained to attend solely to itself, while remaining globally visible to all other tokens. Experimental results demonstrate that introducing a single extra token stabilizes attention sinks, substantially improving model performance. Crucially, further analysis confirms that the effectiveness of this token is independent of its position and characterized by negligible semantic content, validating its role as a robust and dedicated structural sink.

Diffusion models have demonstrated exceptional capability in generating high-quality images, videos, and audio. Due to their adaptiveness in iterative refinement, they provide a strong potential for achieving better non-autoregressive sequence generation. However, existing text diffusion models still fall short in their performance due to a challenge in handling the discreteness of language. This paper thoroughly analyzes text diffusion models and uncovers two significant limitations: degradation of self-conditioning during training and misalignment between training and sampling. Motivated by our findings, we propose a novel Text Diffusion model called TREC, which mitigates the degradation with Reinforced Conditioning and the misalignment by Time-Aware Variance Scaling. Our extensive experiments demonstrate the competitiveness of TREC against autoregressive, non-autoregressive, and diffusion baselines. Moreover, qualitative analysis shows its advanced ability to fully utilize the diffusion process in refining samples.

In recent years, diffusion based methods have emerged as a powerful paradigm for generative modeling. Although discrete diffusion for natural language processing has been explored to a lesser extent, it shows promise for tasks requiring iterative denoising of token based data. In standard approaches to text generation, transformers dominate, but their reliance on self attention often incurs high computational costs. This paper introduces a fully diffusion driven discrete text generation model built without any transformer or large convolution modules. Instead, the model integrates structured state space dynamics in the time domain with a novel Complex Fourier Multi Layer Perceptron module that operates in the frequency domain. The forward noising process randomly samples the vocabulary to replace tokens with a controlled probability, while the learned reverse model systematically reverts corrupted sequences toward their original states. By composing local state space updates with global Fourier based mixing, the approach effectively captures both short and long range dependencies.

Diffusion Language Models (DLMs) present a compelling alternative to autoregressive models, offering flexible, any-order infilling without specialized prompting design. However, their practical utility is blocked by a critical limitation: the requirement of a fixed-length masked sequence for generation. This constraint severely degrades code infilling performance when the predefined mask size mismatches the ideal completion length. To address this, we propose DreamOn, a novel diffusion framework that enables dynamic, variable-length generation. DreamOn augments the diffusion process with two length control states, allowing the model to autonomously expand or contract the output length based solely on its own predictions. We integrate this mechanism into existing DLMs with minimal modifications to the training objective and no architectural changes. Built upon Dream-Coder-7B and DiffuCoder-7B, DreamOn achieves infilling performance on par with state-of-the-art autoregressive models on HumanEval-Infilling and SantaCoder-FIM and matches oracle performance achieved with ground-truth length. Our work removes a fundamental barrier to the practical deployment of DLMs, significantly advancing their flexibility and applicability for variable-length generation. Our code is available at https://github.com/DreamLM/DreamOn.

Diffusion language models (DLMs) have recently demonstrated capabilities that complement standard autoregressive (AR) models, particularly in non-sequential generation and bidirectional editing. Although recent work has shown that pretrained autoregressive checkpoints can be converted into diffusion language models, existing recipes primarily transfer parameters through continued denoising training with objective- and attention-level modifications. We instead ask whether the internal representation geometry learned by next-token prediction can be explicitly preserved during AR-to-DLM conversion. We hypothesize that much of the semantic structure learned by AR pretraining can transfer across generation orders, and thus DLM training should be viewed as relearning the decoding path rather than relearning language representations. To investigate this, we introduce REPR-ALIGN, a representation alignment objective that adapts a bidirectional masked diffusion model to reuse representations from a pretrained AR model of identical architecture. Concretely, we align the hidden states of the DLM to the frozen AR model at every layer using cosine similarity, while optimizing the standard masked denoising objective. This simple alignment, with no adapters and no architectural changes beyond the attention mask, yields up to 4x training acceleration in our setting and is particularly effective in low-data regimes. Our results suggest that linguistic representations can transfer across generation order, and that representation alignment provides a simple and effective technique for training diffusion language models. Code is available at https://github.com/pengzhangzhi/Open-dLLM.

We present T^star, a simple TraceRL-based training curriculum for progressive block-size scaling in masked diffusion language models (MDMs). Starting from an AR-initialized small-block MDM, T^star transitions smoothly to larger blocks, enabling higher-parallelism decoding with minimal performance degradation on math reasoning benchmarks. Moreover, further analysis suggests that T^star may actually converge to an alternative decoding schedule that achieves comparable performance.

Diffusion language models (dLMs) have emerged as a promising paradigm that enables parallel, non-autoregressive generation, but their learning efficiency lags behind that of autoregressive (AR) language models when trained from scratch. To this end, we study AR-to-dLM conversion to transform pretrained AR models into efficient dLMs that excel in speed while preserving AR models' task accuracy. We achieve this by identifying limitations in the attention patterns and objectives of existing AR-to-dLM methods and then proposing principles and methodologies for more effective AR-to-dLM conversion. Specifically, we first systematically compare different attention patterns and find that maintaining pretrained AR weight distributions is critical for effective AR-to-dLM conversion. As such, we introduce a continuous pretraining scheme with a block-wise attention pattern, which remains causal across blocks while enabling bidirectional modeling within each block. We find that this approach can better preserve pretrained AR models' weight distributions than fully bidirectional modeling, in addition to its known benefit of enabling KV caching, and leads to a win-win in accuracy and efficiency. Second, to mitigate the training-test gap in mask token distributions (uniform vs. highly left-to-right), we propose a position-dependent token masking strategy that assigns higher masking probabilities to later tokens during training to better mimic test-time behavior. Leveraging this framework, we conduct extensive studies of dLMs' attention patterns, training dynamics, and other design choices, providing actionable insights into scalable AR-to-dLM conversion. These studies lead to the Efficient-DLM family, which outperforms state-of-the-art AR models and dLMs, e.g., our Efficient-DLM 8B achieves +5.4%/+2.7% higher accuracy with 4.5x/2.7x higher throughput compared to Dream 7B and Qwen3 4B, respectively.

Large Language Models (LLMs) have shown growing potential in molecular sciences, but they often produce chemically inaccurate descriptions and struggle to recognize or justify potential errors. This raises important concerns about their robustness and reliability in scientific applications. To support more rigorous evaluation of LLMs in chemical reasoning, we present the MolErr2Fix benchmark, designed to assess LLMs on error detection and correction in molecular descriptions. Unlike existing benchmarks focused on molecule-to-text generation or property prediction, MolErr2Fix emphasizes fine-grained chemical understanding. It tasks LLMs with identifying, localizing, explaining, and revising potential structural and semantic errors in molecular descriptions. Specifically, MolErr2Fix consists of 1,193 fine-grained annotated error instances. Each instance contains quadruple annotations, i.e,. (error type, span location, the explanation, and the correction). These tasks are intended to reflect the types of reasoning and verification required in real-world chemical communication. Evaluations of current state-of-the-art LLMs reveal notable performance gaps, underscoring the need for more robust chemical reasoning capabilities. MolErr2Fix provides a focused benchmark for evaluating such capabilities and aims to support progress toward more reliable and chemically informed language models. All annotations and an accompanying evaluation API will be publicly released to facilitate future research.