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stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10. euler_at_final (`bool`, defaults to `False`): Whether to use Euler's method in the final step. It is a trade-off between numerical stability and detail richness. This can stabilize the sampling of the SDE variant of DPMSolver for small number of inference steps, but sometimes may result in blurring. final_sigmas_type (`str`, defaults to `"zero"`): The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0. """
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_compatibles = [] order = 1 @register_to_config def __init__( self, sigma_min: float = 0.3, sigma_max: float = 500, sigma_data: float = 1.0, sigma_schedule: str = "exponential", num_train_timesteps: int = 1000, solver_order: int = 2, prediction_type: str = "v_prediction", rho: float = 7.0, solver_type: str = "midpoint", lower_order_final: bool = True, euler_at_final: bool = False, final_sigmas_type: Optional[str] = "zero", # "zero", "sigma_min" ): if solver_type not in ["midpoint", "heun"]: if solver_type in ["logrho", "bh1", "bh2"]: self.register_to_config(solver_type="midpoint") else: raise NotImplementedError(f"{solver_type} is not implemented for {self.__class__}")
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ramp = torch.linspace(0, 1, num_train_timesteps) if sigma_schedule == "karras": sigmas = self._compute_karras_sigmas(ramp) elif sigma_schedule == "exponential": sigmas = self._compute_exponential_sigmas(ramp) self.timesteps = self.precondition_noise(sigmas) self.sigmas = torch.cat([sigmas, torch.zeros(1, device=sigmas.device)]) # setable values self.num_inference_steps = None self.model_outputs = [None] * solver_order self.lower_order_nums = 0 self._step_index = None self._begin_index = None self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication @property def init_noise_sigma(self): # standard deviation of the initial noise distribution return (self.config.sigma_max**2 + 1) ** 0.5
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@property def step_index(self): """ The index counter for current timestep. It will increase 1 after each scheduler step. """ return self._step_index @property def begin_index(self): """ The index for the first timestep. It should be set from pipeline with `set_begin_index` method. """ return self._begin_index # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index def set_begin_index(self, begin_index: int = 0): """ Sets the begin index for the scheduler. This function should be run from pipeline before the inference. Args: begin_index (`int`): The begin index for the scheduler. """ self._begin_index = begin_index
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# Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler.precondition_inputs def precondition_inputs(self, sample, sigma): c_in = 1 / ((sigma**2 + self.config.sigma_data**2) ** 0.5) scaled_sample = sample * c_in return scaled_sample def precondition_noise(self, sigma): if not isinstance(sigma, torch.Tensor): sigma = torch.tensor([sigma]) return sigma.atan() / math.pi * 2 # Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler.precondition_outputs def precondition_outputs(self, sample, model_output, sigma): sigma_data = self.config.sigma_data c_skip = sigma_data**2 / (sigma**2 + sigma_data**2)
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if self.config.prediction_type == "epsilon": c_out = sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5 elif self.config.prediction_type == "v_prediction": c_out = -sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5 else: raise ValueError(f"Prediction type {self.config.prediction_type} is not supported.") denoised = c_skip * sample + c_out * model_output return denoised # Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler.scale_model_input def scale_model_input(self, sample: torch.Tensor, timestep: Union[float, torch.Tensor]) -> torch.Tensor: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.
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Args: sample (`torch.Tensor`): The input sample. timestep (`int`, *optional*): The current timestep in the diffusion chain. Returns: `torch.Tensor`: A scaled input sample. """ if self.step_index is None: self._init_step_index(timestep) sigma = self.sigmas[self.step_index] sample = self.precondition_inputs(sample, sigma) self.is_scale_input_called = True return sample def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torch.device] = None): """ Sets the discrete timesteps used for the diffusion chain (to be run before inference).
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Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. device (`str` or `torch.device`, *optional*): The device to which the timesteps should be moved to. If `None`, the timesteps are not moved. """ self.num_inference_steps = num_inference_steps ramp = torch.linspace(0, 1, self.num_inference_steps) if self.config.sigma_schedule == "karras": sigmas = self._compute_karras_sigmas(ramp) elif self.config.sigma_schedule == "exponential": sigmas = self._compute_exponential_sigmas(ramp) sigmas = sigmas.to(dtype=torch.float32, device=device) self.timesteps = self.precondition_noise(sigmas)
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if self.config.final_sigmas_type == "sigma_min": sigma_last = self.config.sigma_min elif self.config.final_sigmas_type == "zero": sigma_last = 0 else: raise ValueError( f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}" ) self.sigmas = torch.cat([sigmas, torch.tensor([sigma_last], dtype=torch.float32, device=device)]) self.model_outputs = [ None, ] * self.config.solver_order self.lower_order_nums = 0 # add an index counter for schedulers that allow duplicated timesteps self._step_index = None self._begin_index = None self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication # if a noise sampler is used, reinitialise it self.noise_sampler = None
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# Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler._compute_karras_sigmas def _compute_karras_sigmas(self, ramp, sigma_min=None, sigma_max=None) -> torch.Tensor: """Constructs the noise schedule of Karras et al. (2022).""" sigma_min = sigma_min or self.config.sigma_min sigma_max = sigma_max or self.config.sigma_max rho = self.config.rho min_inv_rho = sigma_min ** (1 / rho) max_inv_rho = sigma_max ** (1 / rho) sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho return sigmas # Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler._compute_exponential_sigmas def _compute_exponential_sigmas(self, ramp, sigma_min=None, sigma_max=None) -> torch.Tensor: """Implementation closely follows k-diffusion.
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https://github.com/crowsonkb/k-diffusion/blob/6ab5146d4a5ef63901326489f31f1d8e7dd36b48/k_diffusion/sampling.py#L26 """ sigma_min = sigma_min or self.config.sigma_min sigma_max = sigma_max or self.config.sigma_max sigmas = torch.linspace(math.log(sigma_min), math.log(sigma_max), len(ramp)).exp().flip(0) return sigmas # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t def _sigma_to_t(self, sigma, log_sigmas): # get log sigma log_sigma = np.log(np.maximum(sigma, 1e-10)) # get distribution dists = log_sigma - log_sigmas[:, np.newaxis] # get sigmas range low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2) high_idx = low_idx + 1 low = log_sigmas[low_idx] high = log_sigmas[high_idx] # interpolate sigmas w = (low - log_sigma) / (low - high) w = np.clip(w, 0, 1)
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# transform interpolation to time range t = (1 - w) * low_idx + w * high_idx t = t.reshape(sigma.shape) return t def _sigma_to_alpha_sigma_t(self, sigma): alpha_t = torch.tensor(1) # Inputs are pre-scaled before going into unet, so alpha_t = 1 sigma_t = sigma return alpha_t, sigma_t def convert_model_output( self, model_output: torch.Tensor, sample: torch.Tensor = None, ) -> torch.Tensor: """ Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an integral of the data prediction model. <Tip> The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise prediction and data prediction models. </Tip>
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Args: model_output (`torch.Tensor`): The direct output from the learned diffusion model. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. Returns: `torch.Tensor`: The converted model output. """ sigma = self.sigmas[self.step_index] x0_pred = self.precondition_outputs(sample, model_output, sigma) return x0_pred def dpm_solver_first_order_update( self, model_output: torch.Tensor, sample: torch.Tensor = None, noise: Optional[torch.Tensor] = None, ) -> torch.Tensor: """ One step for the first-order DPMSolver (equivalent to DDIM). Args: model_output (`torch.Tensor`): The direct output from the learned diffusion model. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process.
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Returns: `torch.Tensor`: The sample tensor at the previous timestep. """ sigma_t, sigma_s = self.sigmas[self.step_index + 1], self.sigmas[self.step_index] alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t) alpha_s, sigma_s = self._sigma_to_alpha_sigma_t(sigma_s) lambda_t = torch.log(alpha_t) - torch.log(sigma_t) lambda_s = torch.log(alpha_s) - torch.log(sigma_s) h = lambda_t - lambda_s assert noise is not None x_t = ( (sigma_t / sigma_s * torch.exp(-h)) * sample + (alpha_t * (1 - torch.exp(-2.0 * h))) * model_output + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise ) return x_t
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def multistep_dpm_solver_second_order_update( self, model_output_list: List[torch.Tensor], sample: torch.Tensor = None, noise: Optional[torch.Tensor] = None, ) -> torch.Tensor: """ One step for the second-order multistep DPMSolver. Args: model_output_list (`List[torch.Tensor]`): The direct outputs from learned diffusion model at current and latter timesteps. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. Returns: `torch.Tensor`: The sample tensor at the previous timestep. """ sigma_t, sigma_s0, sigma_s1 = ( self.sigmas[self.step_index + 1], self.sigmas[self.step_index], self.sigmas[self.step_index - 1], )
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alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t) alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0) alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1) lambda_t = torch.log(alpha_t) - torch.log(sigma_t) lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0) lambda_s1 = torch.log(alpha_s1) - torch.log(sigma_s1) m0, m1 = model_output_list[-1], model_output_list[-2] h, h_0 = lambda_t - lambda_s0, lambda_s0 - lambda_s1 r0 = h_0 / h D0, D1 = m0, (1.0 / r0) * (m0 - m1)
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# sde-dpmsolver++ assert noise is not None if self.config.solver_type == "midpoint": x_t = ( (sigma_t / sigma_s0 * torch.exp(-h)) * sample + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0 + 0.5 * (alpha_t * (1 - torch.exp(-2.0 * h))) * D1 + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise ) elif self.config.solver_type == "heun": x_t = ( (sigma_t / sigma_s0 * torch.exp(-h)) * sample + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0 + (alpha_t * ((1.0 - torch.exp(-2.0 * h)) / (-2.0 * h) + 1.0)) * D1 + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise ) return x_t
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# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.index_for_timestep def index_for_timestep(self, timestep, schedule_timesteps=None): if schedule_timesteps is None: schedule_timesteps = self.timesteps index_candidates = (schedule_timesteps == timestep).nonzero() if len(index_candidates) == 0: step_index = len(self.timesteps) - 1 # The sigma index that is taken for the **very** first `step` # is always the second index (or the last index if there is only 1) # This way we can ensure we don't accidentally skip a sigma in # case we start in the middle of the denoising schedule (e.g. for image-to-image) elif len(index_candidates) > 1: step_index = index_candidates[1].item() else: step_index = index_candidates[0].item() return step_index
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# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index def _init_step_index(self, timestep): """ Initialize the step_index counter for the scheduler. """ if self.begin_index is None: if isinstance(timestep, torch.Tensor): timestep = timestep.to(self.timesteps.device) self._step_index = self.index_for_timestep(timestep) else: self._step_index = self._begin_index def step( self, model_output: torch.Tensor, timestep: Union[int, torch.Tensor], sample: torch.Tensor, generator=None, return_dict: bool = True, ) -> Union[SchedulerOutput, Tuple]: """ Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with the multistep DPMSolver.
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Args: model_output (`torch.Tensor`): The direct output from learned diffusion model. timestep (`int`): The current discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. generator (`torch.Generator`, *optional*): A random number generator. return_dict (`bool`): Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`. Returns: [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor.
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""" if self.num_inference_steps is None: raise ValueError( "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" ) if self.step_index is None: self._init_step_index(timestep) # Improve numerical stability for small number of steps lower_order_final = (self.step_index == len(self.timesteps) - 1) and ( self.config.euler_at_final or (self.config.lower_order_final and len(self.timesteps) < 15) or self.config.final_sigmas_type == "zero" ) lower_order_second = ( (self.step_index == len(self.timesteps) - 2) and self.config.lower_order_final and len(self.timesteps) < 15 )
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model_output = self.convert_model_output(model_output, sample=sample) for i in range(self.config.solver_order - 1): self.model_outputs[i] = self.model_outputs[i + 1] self.model_outputs[-1] = model_output if self.noise_sampler is None: seed = None if generator is not None: seed = ( [g.initial_seed() for g in generator] if isinstance(generator, list) else generator.initial_seed() ) self.noise_sampler = BrownianTreeNoiseSampler( model_output, sigma_min=self.config.sigma_min, sigma_max=self.config.sigma_max, seed=seed ) noise = self.noise_sampler(self.sigmas[self.step_index], self.sigmas[self.step_index + 1]).to( model_output.device )
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if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final: prev_sample = self.dpm_solver_first_order_update(model_output, sample=sample, noise=noise) elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second: prev_sample = self.multistep_dpm_solver_second_order_update(self.model_outputs, sample=sample, noise=noise) if self.lower_order_nums < self.config.solver_order: self.lower_order_nums += 1 # upon completion increase step index by one self._step_index += 1 if not return_dict: return (prev_sample,) return SchedulerOutput(prev_sample=prev_sample)
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# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise def add_noise( self, original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.Tensor, ) -> torch.Tensor: # Make sure sigmas and timesteps have the same device and dtype as original_samples sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype) if original_samples.device.type == "mps" and torch.is_floating_point(timesteps): # mps does not support float64 schedule_timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32) timesteps = timesteps.to(original_samples.device, dtype=torch.float32) else: schedule_timesteps = self.timesteps.to(original_samples.device) timesteps = timesteps.to(original_samples.device)
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# self.begin_index is None when scheduler is used for training, or pipeline does not implement set_begin_index if self.begin_index is None: step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps] elif self.step_index is not None: # add_noise is called after first denoising step (for inpainting) step_indices = [self.step_index] * timesteps.shape[0] else: # add noise is called before first denoising step to create initial latent(img2img) step_indices = [self.begin_index] * timesteps.shape[0] sigma = sigmas[step_indices].flatten() while len(sigma.shape) < len(original_samples.shape): sigma = sigma.unsqueeze(-1) noisy_samples = original_samples + noise * sigma return noisy_samples def __len__(self): return self.config.num_train_timesteps
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class LCMSchedulerOutput(BaseOutput): """ Output class for the scheduler's `step` function output. Args: prev_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the denoising loop. pred_original_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): The predicted denoised sample `(x_{0})` based on the model output from the current timestep. `pred_original_sample` can be used to preview progress or for guidance. """ prev_sample: torch.Tensor denoised: Optional[torch.Tensor] = None
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class LCMScheduler(SchedulerMixin, ConfigMixin): """ `LCMScheduler` extends the denoising procedure introduced in denoising diffusion probabilistic models (DDPMs) with non-Markovian guidance. This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__` function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`. [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and [`~SchedulerMixin.from_pretrained`] functions.
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Args: num_train_timesteps (`int`, defaults to 1000): The number of diffusion steps to train the model. beta_start (`float`, defaults to 0.0001): The starting `beta` value of inference. beta_end (`float`, defaults to 0.02): The final `beta` value. beta_schedule (`str`, defaults to `"linear"`): The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from `linear`, `scaled_linear`, or `squaredcos_cap_v2`. trained_betas (`np.ndarray`, *optional*): Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`. original_inference_steps (`int`, *optional*, defaults to 50): The default number of inference steps used to generate a linearly-spaced timestep schedule, from which we will ultimately take `num_inference_steps` evenly spaced timesteps to form the final timestep schedule.
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clip_sample (`bool`, defaults to `True`): Clip the predicted sample for numerical stability. clip_sample_range (`float`, defaults to 1.0): The maximum magnitude for sample clipping. Valid only when `clip_sample=True`. set_alpha_to_one (`bool`, defaults to `True`): Each diffusion step uses the alphas product value at that step and at the previous one. For the final step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`, otherwise it uses the alpha value at step 0. steps_offset (`int`, defaults to 0): An offset added to the inference steps, as required by some model families. prediction_type (`str`, defaults to `epsilon`, *optional*): Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
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`sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen Video](https://imagen.research.google/video/paper.pdf) paper). thresholding (`bool`, defaults to `False`): Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such as Stable Diffusion. dynamic_thresholding_ratio (`float`, defaults to 0.995): The ratio for the dynamic thresholding method. Valid only when `thresholding=True`. sample_max_value (`float`, defaults to 1.0): The threshold value for dynamic thresholding. Valid only when `thresholding=True`. timestep_spacing (`str`, defaults to `"leading"`): The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information. timestep_scaling (`float`, defaults to 10.0):
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The factor the timesteps will be multiplied by when calculating the consistency model boundary conditions `c_skip` and `c_out`. Increasing this will decrease the approximation error (although the approximation error at the default of `10.0` is already pretty small). rescale_betas_zero_snr (`bool`, defaults to `False`): Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and dark samples instead of limiting it to samples with medium brightness. Loosely related to [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506). """
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order = 1
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@register_to_config def __init__( self, num_train_timesteps: int = 1000, beta_start: float = 0.00085, beta_end: float = 0.012, beta_schedule: str = "scaled_linear", trained_betas: Optional[Union[np.ndarray, List[float]]] = None, original_inference_steps: int = 50, clip_sample: bool = False, clip_sample_range: float = 1.0, set_alpha_to_one: bool = True, steps_offset: int = 0, prediction_type: str = "epsilon", thresholding: bool = False, dynamic_thresholding_ratio: float = 0.995, sample_max_value: float = 1.0, timestep_spacing: str = "leading", timestep_scaling: float = 10.0, rescale_betas_zero_snr: bool = False, ): if trained_betas is not None: self.betas = torch.tensor(trained_betas, dtype=torch.float32) elif beta_schedule == "linear":
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self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32) elif beta_schedule == "scaled_linear": # this schedule is very specific to the latent diffusion model. self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2 elif beta_schedule == "squaredcos_cap_v2": # Glide cosine schedule self.betas = betas_for_alpha_bar(num_train_timesteps) else: raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")
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# Rescale for zero SNR if rescale_betas_zero_snr: self.betas = rescale_zero_terminal_snr(self.betas) self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) # At every step in ddim, we are looking into the previous alphas_cumprod # For the final step, there is no previous alphas_cumprod because we are already at 0 # `set_alpha_to_one` decides whether we set this parameter simply to one or # whether we use the final alpha of the "non-previous" one. self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0] # standard deviation of the initial noise distribution self.init_noise_sigma = 1.0 # setable values self.num_inference_steps = None self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy().astype(np.int64)) self.custom_timesteps = False
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self._step_index = None self._begin_index = None # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep def index_for_timestep(self, timestep, schedule_timesteps=None): if schedule_timesteps is None: schedule_timesteps = self.timesteps indices = (schedule_timesteps == timestep).nonzero() # The sigma index that is taken for the **very** first `step` # is always the second index (or the last index if there is only 1) # This way we can ensure we don't accidentally skip a sigma in # case we start in the middle of the denoising schedule (e.g. for image-to-image) pos = 1 if len(indices) > 1 else 0 return indices[pos].item()
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# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index def _init_step_index(self, timestep): if self.begin_index is None: if isinstance(timestep, torch.Tensor): timestep = timestep.to(self.timesteps.device) self._step_index = self.index_for_timestep(timestep) else: self._step_index = self._begin_index @property def step_index(self): return self._step_index @property def begin_index(self): """ The index for the first timestep. It should be set from pipeline with `set_begin_index` method. """ return self._begin_index # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index def set_begin_index(self, begin_index: int = 0): """ Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
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Args: begin_index (`int`): The begin index for the scheduler. """ self._begin_index = begin_index def scale_model_input(self, sample: torch.Tensor, timestep: Optional[int] = None) -> torch.Tensor: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. Args: sample (`torch.Tensor`): The input sample. timestep (`int`, *optional*): The current timestep in the diffusion chain. Returns: `torch.Tensor`: A scaled input sample. """ return sample
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# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor: """ "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing pixels from saturation at each step. We find that dynamic thresholding results in significantly better photorealism as well as better image-text alignment, especially when using very large guidance weights." https://arxiv.org/abs/2205.11487 """ dtype = sample.dtype batch_size, channels, *remaining_dims = sample.shape
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if dtype not in (torch.float32, torch.float64): sample = sample.float() # upcast for quantile calculation, and clamp not implemented for cpu half # Flatten sample for doing quantile calculation along each image sample = sample.reshape(batch_size, channels * np.prod(remaining_dims)) abs_sample = sample.abs() # "a certain percentile absolute pixel value" s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1) s = torch.clamp( s, min=1, max=self.config.sample_max_value ) # When clamped to min=1, equivalent to standard clipping to [-1, 1] s = s.unsqueeze(1) # (batch_size, 1) because clamp will broadcast along dim=0 sample = torch.clamp(sample, -s, s) / s # "we threshold xt0 to the range [-s, s] and then divide by s" sample = sample.reshape(batch_size, channels, *remaining_dims) sample = sample.to(dtype) return sample
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def set_timesteps( self, num_inference_steps: Optional[int] = None, device: Union[str, torch.device] = None, original_inference_steps: Optional[int] = None, timesteps: Optional[List[int]] = None, strength: int = 1.0, ): """ Sets the discrete timesteps used for the diffusion chain (to be run before inference).
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Args: num_inference_steps (`int`, *optional*): The number of diffusion steps used when generating samples with a pre-trained model. If used, `timesteps` must be `None`. device (`str` or `torch.device`, *optional*): The device to which the timesteps should be moved to. If `None`, the timesteps are not moved. original_inference_steps (`int`, *optional*): The original number of inference steps, which will be used to generate a linearly-spaced timestep schedule (which is different from the standard `diffusers` implementation). We will then take `num_inference_steps` timesteps from this schedule, evenly spaced in terms of indices, and use that as our final timestep schedule. If not set, this will default to the `original_inference_steps` attribute. timesteps (`List[int]`, *optional*):
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Custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default timestep spacing strategy of equal spacing between timesteps on the training/distillation timestep schedule is used. If `timesteps` is passed, `num_inference_steps` must be `None`. """ # 0. Check inputs if num_inference_steps is None and timesteps is None: raise ValueError("Must pass exactly one of `num_inference_steps` or `custom_timesteps`.")
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if num_inference_steps is not None and timesteps is not None: raise ValueError("Can only pass one of `num_inference_steps` or `custom_timesteps`.") # 1. Calculate the LCM original training/distillation timestep schedule. original_steps = ( original_inference_steps if original_inference_steps is not None else self.config.original_inference_steps ) if original_steps > self.config.num_train_timesteps: raise ValueError( f"`original_steps`: {original_steps} cannot be larger than `self.config.train_timesteps`:" f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle" f" maximal {self.config.num_train_timesteps} timesteps." )
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# LCM Timesteps Setting # The skipping step parameter k from the paper. k = self.config.num_train_timesteps // original_steps # LCM Training/Distillation Steps Schedule # Currently, only a linearly-spaced schedule is supported (same as in the LCM distillation scripts). lcm_origin_timesteps = np.asarray(list(range(1, int(original_steps * strength) + 1))) * k - 1 # 2. Calculate the LCM inference timestep schedule. if timesteps is not None: # 2.1 Handle custom timestep schedules. train_timesteps = set(lcm_origin_timesteps) non_train_timesteps = [] for i in range(1, len(timesteps)): if timesteps[i] >= timesteps[i - 1]: raise ValueError("`custom_timesteps` must be in descending order.") if timesteps[i] not in train_timesteps: non_train_timesteps.append(timesteps[i])
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if timesteps[0] >= self.config.num_train_timesteps: raise ValueError( f"`timesteps` must start before `self.config.train_timesteps`:" f" {self.config.num_train_timesteps}." ) # Raise warning if timestep schedule does not start with self.config.num_train_timesteps - 1 if strength == 1.0 and timesteps[0] != self.config.num_train_timesteps - 1: logger.warning( f"The first timestep on the custom timestep schedule is {timesteps[0]}, not" f" `self.config.num_train_timesteps - 1`: {self.config.num_train_timesteps - 1}. You may get" f" unexpected results when using this timestep schedule." )
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# Raise warning if custom timestep schedule contains timesteps not on original timestep schedule if non_train_timesteps: logger.warning( f"The custom timestep schedule contains the following timesteps which are not on the original" f" training/distillation timestep schedule: {non_train_timesteps}. You may get unexpected results" f" when using this timestep schedule." ) # Raise warning if custom timestep schedule is longer than original_steps if len(timesteps) > original_steps: logger.warning( f"The number of timesteps in the custom timestep schedule is {len(timesteps)}, which exceeds the" f" the length of the timestep schedule used for training: {original_steps}. You may get some" f" unexpected results when using this timestep schedule." )
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timesteps = np.array(timesteps, dtype=np.int64) self.num_inference_steps = len(timesteps) self.custom_timesteps = True
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# Apply strength (e.g. for img2img pipelines) (see StableDiffusionImg2ImgPipeline.get_timesteps) init_timestep = min(int(self.num_inference_steps * strength), self.num_inference_steps) t_start = max(self.num_inference_steps - init_timestep, 0) timesteps = timesteps[t_start * self.order :] # TODO: also reset self.num_inference_steps? else: # 2.2 Create the "standard" LCM inference timestep schedule. if num_inference_steps > self.config.num_train_timesteps: raise ValueError( f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:" f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle" f" maximal {self.config.num_train_timesteps} timesteps." ) skipping_step = len(lcm_origin_timesteps) // num_inference_steps
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if skipping_step < 1: raise ValueError( f"The combination of `original_steps x strength`: {original_steps} x {strength} is smaller than `num_inference_steps`: {num_inference_steps}. Make sure to either reduce `num_inference_steps` to a value smaller than {int(original_steps * strength)} or increase `strength` to a value higher than {float(num_inference_steps / original_steps)}." ) self.num_inference_steps = num_inference_steps if num_inference_steps > original_steps: raise ValueError( f"`num_inference_steps`: {num_inference_steps} cannot be larger than `original_inference_steps`:" f" {original_steps} because the final timestep schedule will be a subset of the" f" `original_inference_steps`-sized initial timestep schedule." )
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# LCM Inference Steps Schedule lcm_origin_timesteps = lcm_origin_timesteps[::-1].copy() # Select (approximately) evenly spaced indices from lcm_origin_timesteps. inference_indices = np.linspace(0, len(lcm_origin_timesteps), num=num_inference_steps, endpoint=False) inference_indices = np.floor(inference_indices).astype(np.int64) timesteps = lcm_origin_timesteps[inference_indices] self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.long) self._step_index = None self._begin_index = None def get_scalings_for_boundary_condition_discrete(self, timestep): self.sigma_data = 0.5 # Default: 0.5 scaled_timestep = timestep * self.config.timestep_scaling c_skip = self.sigma_data**2 / (scaled_timestep**2 + self.sigma_data**2) c_out = scaled_timestep / (scaled_timestep**2 + self.sigma_data**2) ** 0.5 return c_skip, c_out
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def step( self, model_output: torch.Tensor, timestep: int, sample: torch.Tensor, generator: Optional[torch.Generator] = None, return_dict: bool = True, ) -> Union[LCMSchedulerOutput, Tuple]: """ Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion process from the learned model outputs (most often the predicted noise).
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Args: model_output (`torch.Tensor`): The direct output from learned diffusion model. timestep (`float`): The current discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. generator (`torch.Generator`, *optional*): A random number generator. return_dict (`bool`, *optional*, defaults to `True`): Whether or not to return a [`~schedulers.scheduling_lcm.LCMSchedulerOutput`] or `tuple`. Returns: [`~schedulers.scheduling_utils.LCMSchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_lcm.LCMSchedulerOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor. """ if self.num_inference_steps is None: raise ValueError(
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"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" )
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if self.step_index is None: self._init_step_index(timestep) # 1. get previous step value prev_step_index = self.step_index + 1 if prev_step_index < len(self.timesteps): prev_timestep = self.timesteps[prev_step_index] else: prev_timestep = timestep # 2. compute alphas, betas alpha_prod_t = self.alphas_cumprod[timestep] alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod beta_prod_t = 1 - alpha_prod_t beta_prod_t_prev = 1 - alpha_prod_t_prev # 3. Get scalings for boundary conditions c_skip, c_out = self.get_scalings_for_boundary_condition_discrete(timestep)
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# 4. Compute the predicted original sample x_0 based on the model parameterization if self.config.prediction_type == "epsilon": # noise-prediction predicted_original_sample = (sample - beta_prod_t.sqrt() * model_output) / alpha_prod_t.sqrt() elif self.config.prediction_type == "sample": # x-prediction predicted_original_sample = model_output elif self.config.prediction_type == "v_prediction": # v-prediction predicted_original_sample = alpha_prod_t.sqrt() * sample - beta_prod_t.sqrt() * model_output else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or" " `v_prediction` for `LCMScheduler`." )
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# 5. Clip or threshold "predicted x_0" if self.config.thresholding: predicted_original_sample = self._threshold_sample(predicted_original_sample) elif self.config.clip_sample: predicted_original_sample = predicted_original_sample.clamp( -self.config.clip_sample_range, self.config.clip_sample_range ) # 6. Denoise model output using boundary conditions denoised = c_out * predicted_original_sample + c_skip * sample
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# 7. Sample and inject noise z ~ N(0, I) for MultiStep Inference # Noise is not used on the final timestep of the timestep schedule. # This also means that noise is not used for one-step sampling. if self.step_index != self.num_inference_steps - 1: noise = randn_tensor( model_output.shape, generator=generator, device=model_output.device, dtype=denoised.dtype ) prev_sample = alpha_prod_t_prev.sqrt() * denoised + beta_prod_t_prev.sqrt() * noise else: prev_sample = denoised # upon completion increase step index by one self._step_index += 1 if not return_dict: return (prev_sample, denoised) return LCMSchedulerOutput(prev_sample=prev_sample, denoised=denoised)
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# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise def add_noise( self, original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor, ) -> torch.Tensor: # Make sure alphas_cumprod and timestep have same device and dtype as original_samples # Move the self.alphas_cumprod to device to avoid redundant CPU to GPU data movement # for the subsequent add_noise calls self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device) alphas_cumprod = self.alphas_cumprod.to(dtype=original_samples.dtype) timesteps = timesteps.to(original_samples.device) sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5 sqrt_alpha_prod = sqrt_alpha_prod.flatten() while len(sqrt_alpha_prod.shape) < len(original_samples.shape): sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
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sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten() while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape): sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1) noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise return noisy_samples # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.get_velocity def get_velocity(self, sample: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor) -> torch.Tensor: # Make sure alphas_cumprod and timestep have same device and dtype as sample self.alphas_cumprod = self.alphas_cumprod.to(device=sample.device) alphas_cumprod = self.alphas_cumprod.to(dtype=sample.dtype) timesteps = timesteps.to(sample.device)
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sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5 sqrt_alpha_prod = sqrt_alpha_prod.flatten() while len(sqrt_alpha_prod.shape) < len(sample.shape): sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1) sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten() while len(sqrt_one_minus_alpha_prod.shape) < len(sample.shape): sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1) velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample return velocity def __len__(self): return self.config.num_train_timesteps
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# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.previous_timestep def previous_timestep(self, timestep): if self.custom_timesteps or self.num_inference_steps: index = (self.timesteps == timestep).nonzero(as_tuple=True)[0][0] if index == self.timesteps.shape[0] - 1: prev_t = torch.tensor(-1) else: prev_t = self.timesteps[index + 1] else: prev_t = timestep - 1 return prev_t
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class DDPMSchedulerOutput(BaseOutput): """ Output class for the scheduler's `step` function output. Args: prev_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the denoising loop. pred_original_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): The predicted denoised sample `(x_{0})` based on the model output from the current timestep. `pred_original_sample` can be used to preview progress or for guidance. """ prev_sample: torch.Tensor pred_original_sample: Optional[torch.Tensor] = None
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class DDPMScheduler(SchedulerMixin, ConfigMixin): """ `DDPMScheduler` explores the connections between denoising score matching and Langevin dynamics sampling. This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic methods the library implements for all schedulers such as loading and saving.
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Args: num_train_timesteps (`int`, defaults to 1000): The number of diffusion steps to train the model. beta_start (`float`, defaults to 0.0001): The starting `beta` value of inference. beta_end (`float`, defaults to 0.02): The final `beta` value. beta_schedule (`str`, defaults to `"linear"`): The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from `linear`, `scaled_linear`, or `squaredcos_cap_v2`. trained_betas (`np.ndarray`, *optional*): An array of betas to pass directly to the constructor without using `beta_start` and `beta_end`. variance_type (`str`, defaults to `"fixed_small"`): Clip the variance when adding noise to the denoised sample. Choose from `fixed_small`, `fixed_small_log`, `fixed_large`, `fixed_large_log`, `learned` or `learned_range`. clip_sample (`bool`, defaults to `True`):
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Clip the predicted sample for numerical stability. clip_sample_range (`float`, defaults to 1.0): The maximum magnitude for sample clipping. Valid only when `clip_sample=True`. prediction_type (`str`, defaults to `epsilon`, *optional*): Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process), `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen Video](https://imagen.research.google/video/paper.pdf) paper). thresholding (`bool`, defaults to `False`): Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such as Stable Diffusion. dynamic_thresholding_ratio (`float`, defaults to 0.995): The ratio for the dynamic thresholding method. Valid only when `thresholding=True`. sample_max_value (`float`, defaults to 1.0):
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The threshold value for dynamic thresholding. Valid only when `thresholding=True`. timestep_spacing (`str`, defaults to `"leading"`): The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information. steps_offset (`int`, defaults to 0): An offset added to the inference steps, as required by some model families. rescale_betas_zero_snr (`bool`, defaults to `False`): Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and dark samples instead of limiting it to samples with medium brightness. Loosely related to [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506). """
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_compatibles = [e.name for e in KarrasDiffusionSchedulers] order = 1
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@register_to_config def __init__( self, num_train_timesteps: int = 1000, beta_start: float = 0.0001, beta_end: float = 0.02, beta_schedule: str = "linear", trained_betas: Optional[Union[np.ndarray, List[float]]] = None, variance_type: str = "fixed_small", clip_sample: bool = True, prediction_type: str = "epsilon", thresholding: bool = False, dynamic_thresholding_ratio: float = 0.995, clip_sample_range: float = 1.0, sample_max_value: float = 1.0, timestep_spacing: str = "leading", steps_offset: int = 0, rescale_betas_zero_snr: bool = False, ): if trained_betas is not None: self.betas = torch.tensor(trained_betas, dtype=torch.float32) elif beta_schedule == "linear": self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32) elif beta_schedule == "scaled_linear":
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# this schedule is very specific to the latent diffusion model. self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2 elif beta_schedule == "squaredcos_cap_v2": # Glide cosine schedule self.betas = betas_for_alpha_bar(num_train_timesteps) elif beta_schedule == "sigmoid": # GeoDiff sigmoid schedule betas = torch.linspace(-6, 6, num_train_timesteps) self.betas = torch.sigmoid(betas) * (beta_end - beta_start) + beta_start else: raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")
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# Rescale for zero SNR if rescale_betas_zero_snr: self.betas = rescale_zero_terminal_snr(self.betas) self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) self.one = torch.tensor(1.0) # standard deviation of the initial noise distribution self.init_noise_sigma = 1.0 # setable values self.custom_timesteps = False self.num_inference_steps = None self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy()) self.variance_type = variance_type def scale_model_input(self, sample: torch.Tensor, timestep: Optional[int] = None) -> torch.Tensor: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep.
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Args: sample (`torch.Tensor`): The input sample. timestep (`int`, *optional*): The current timestep in the diffusion chain. Returns: `torch.Tensor`: A scaled input sample. """ return sample def set_timesteps( self, num_inference_steps: Optional[int] = None, device: Union[str, torch.device] = None, timesteps: Optional[List[int]] = None, ): """ Sets the discrete timesteps used for the diffusion chain (to be run before inference).
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Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. If used, `timesteps` must be `None`. device (`str` or `torch.device`, *optional*): The device to which the timesteps should be moved to. If `None`, the timesteps are not moved. timesteps (`List[int]`, *optional*): Custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default timestep spacing strategy of equal spacing between timesteps is used. If `timesteps` is passed, `num_inference_steps` must be `None`. """ if num_inference_steps is not None and timesteps is not None: raise ValueError("Can only pass one of `num_inference_steps` or `custom_timesteps`.")
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if timesteps is not None: for i in range(1, len(timesteps)): if timesteps[i] >= timesteps[i - 1]: raise ValueError("`custom_timesteps` must be in descending order.") if timesteps[0] >= self.config.num_train_timesteps: raise ValueError( f"`timesteps` must start before `self.config.train_timesteps`:" f" {self.config.num_train_timesteps}." )
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timesteps = np.array(timesteps, dtype=np.int64) self.custom_timesteps = True else: if num_inference_steps > self.config.num_train_timesteps: raise ValueError( f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:" f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle" f" maximal {self.config.num_train_timesteps} timesteps." ) self.num_inference_steps = num_inference_steps self.custom_timesteps = False
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# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891 if self.config.timestep_spacing == "linspace": timesteps = ( np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps) .round()[::-1] .copy() .astype(np.int64) ) elif self.config.timestep_spacing == "leading": step_ratio = self.config.num_train_timesteps // self.num_inference_steps # creates integer timesteps by multiplying by ratio # casting to int to avoid issues when num_inference_step is power of 3 timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.int64) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing":
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step_ratio = self.config.num_train_timesteps / self.num_inference_steps # creates integer timesteps by multiplying by ratio # casting to int to avoid issues when num_inference_step is power of 3 timesteps = np.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio)).astype(np.int64) timesteps -= 1 else: raise ValueError( f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'." )
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self.timesteps = torch.from_numpy(timesteps).to(device) def _get_variance(self, t, predicted_variance=None, variance_type=None): prev_t = self.previous_timestep(t) alpha_prod_t = self.alphas_cumprod[t] alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.one current_beta_t = 1 - alpha_prod_t / alpha_prod_t_prev # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf) # and sample from it to get previous sample # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * current_beta_t # we always take the log of variance, so clamp it to ensure it's not 0 variance = torch.clamp(variance, min=1e-20) if variance_type is None: variance_type = self.config.variance_type
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# hacks - were probably added for training stability if variance_type == "fixed_small": variance = variance # for rl-diffuser https://arxiv.org/abs/2205.09991 elif variance_type == "fixed_small_log": variance = torch.log(variance) variance = torch.exp(0.5 * variance) elif variance_type == "fixed_large": variance = current_beta_t elif variance_type == "fixed_large_log": # Glide max_log variance = torch.log(current_beta_t) elif variance_type == "learned": return predicted_variance elif variance_type == "learned_range": min_log = torch.log(variance) max_log = torch.log(current_beta_t) frac = (predicted_variance + 1) / 2 variance = frac * max_log + (1 - frac) * min_log return variance
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def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor: """ "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing pixels from saturation at each step. We find that dynamic thresholding results in significantly better photorealism as well as better image-text alignment, especially when using very large guidance weights." https://arxiv.org/abs/2205.11487 """ dtype = sample.dtype batch_size, channels, *remaining_dims = sample.shape if dtype not in (torch.float32, torch.float64): sample = sample.float() # upcast for quantile calculation, and clamp not implemented for cpu half
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# Flatten sample for doing quantile calculation along each image sample = sample.reshape(batch_size, channels * np.prod(remaining_dims)) abs_sample = sample.abs() # "a certain percentile absolute pixel value" s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1) s = torch.clamp( s, min=1, max=self.config.sample_max_value ) # When clamped to min=1, equivalent to standard clipping to [-1, 1] s = s.unsqueeze(1) # (batch_size, 1) because clamp will broadcast along dim=0 sample = torch.clamp(sample, -s, s) / s # "we threshold xt0 to the range [-s, s] and then divide by s" sample = sample.reshape(batch_size, channels, *remaining_dims) sample = sample.to(dtype) return sample
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def step( self, model_output: torch.Tensor, timestep: int, sample: torch.Tensor, generator=None, return_dict: bool = True, ) -> Union[DDPMSchedulerOutput, Tuple]: """ Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion process from the learned model outputs (most often the predicted noise).
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Args: model_output (`torch.Tensor`): The direct output from learned diffusion model. timestep (`float`): The current discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. generator (`torch.Generator`, *optional*): A random number generator. return_dict (`bool`, *optional*, defaults to `True`): Whether or not to return a [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`. Returns: [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor. """ t = timestep prev_t = self.previous_timestep(t)
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if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]: model_output, predicted_variance = torch.split(model_output, sample.shape[1], dim=1) else: predicted_variance = None # 1. compute alphas, betas alpha_prod_t = self.alphas_cumprod[t] alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.one beta_prod_t = 1 - alpha_prod_t beta_prod_t_prev = 1 - alpha_prod_t_prev current_alpha_t = alpha_prod_t / alpha_prod_t_prev current_beta_t = 1 - current_alpha_t
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# 2. compute predicted original sample from predicted noise also called # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf if self.config.prediction_type == "epsilon": pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5) elif self.config.prediction_type == "sample": pred_original_sample = model_output elif self.config.prediction_type == "v_prediction": pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or" " `v_prediction` for the DDPMScheduler." )
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# 3. Clip or threshold "predicted x_0" if self.config.thresholding: pred_original_sample = self._threshold_sample(pred_original_sample) elif self.config.clip_sample: pred_original_sample = pred_original_sample.clamp( -self.config.clip_sample_range, self.config.clip_sample_range ) # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf pred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * current_beta_t) / beta_prod_t current_sample_coeff = current_alpha_t ** (0.5) * beta_prod_t_prev / beta_prod_t # 5. Compute predicted previous sample µ_t # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf pred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample
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# 6. Add noise variance = 0 if t > 0: device = model_output.device variance_noise = randn_tensor( model_output.shape, generator=generator, device=device, dtype=model_output.dtype ) if self.variance_type == "fixed_small_log": variance = self._get_variance(t, predicted_variance=predicted_variance) * variance_noise elif self.variance_type == "learned_range": variance = self._get_variance(t, predicted_variance=predicted_variance) variance = torch.exp(0.5 * variance) * variance_noise else: variance = (self._get_variance(t, predicted_variance=predicted_variance) ** 0.5) * variance_noise pred_prev_sample = pred_prev_sample + variance if not return_dict: return ( pred_prev_sample, pred_original_sample, )
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return DDPMSchedulerOutput(prev_sample=pred_prev_sample, pred_original_sample=pred_original_sample) def add_noise( self, original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor, ) -> torch.Tensor: # Make sure alphas_cumprod and timestep have same device and dtype as original_samples # Move the self.alphas_cumprod to device to avoid redundant CPU to GPU data movement # for the subsequent add_noise calls self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device) alphas_cumprod = self.alphas_cumprod.to(dtype=original_samples.dtype) timesteps = timesteps.to(original_samples.device) sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5 sqrt_alpha_prod = sqrt_alpha_prod.flatten() while len(sqrt_alpha_prod.shape) < len(original_samples.shape): sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
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sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten() while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape): sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1) noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise return noisy_samples def get_velocity(self, sample: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor) -> torch.Tensor: # Make sure alphas_cumprod and timestep have same device and dtype as sample self.alphas_cumprod = self.alphas_cumprod.to(device=sample.device) alphas_cumprod = self.alphas_cumprod.to(dtype=sample.dtype) timesteps = timesteps.to(sample.device)
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sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5 sqrt_alpha_prod = sqrt_alpha_prod.flatten() while len(sqrt_alpha_prod.shape) < len(sample.shape): sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1) sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten() while len(sqrt_one_minus_alpha_prod.shape) < len(sample.shape): sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1) velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample return velocity def __len__(self): return self.config.num_train_timesteps
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def previous_timestep(self, timestep): if self.custom_timesteps or self.num_inference_steps: index = (self.timesteps == timestep).nonzero(as_tuple=True)[0][0] if index == self.timesteps.shape[0] - 1: prev_t = torch.tensor(-1) else: prev_t = self.timesteps[index + 1] else: prev_t = timestep - 1 return prev_t
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class HeunDiscreteSchedulerOutput(BaseOutput): """ Output class for the scheduler's `step` function output. Args: prev_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the denoising loop. pred_original_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): The predicted denoised sample `(x_{0})` based on the model output from the current timestep. `pred_original_sample` can be used to preview progress or for guidance. """ prev_sample: torch.Tensor pred_original_sample: Optional[torch.Tensor] = None
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class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin): """ Scheduler with Heun steps for discrete beta schedules. This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic methods the library implements for all schedulers such as loading and saving.
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Args: num_train_timesteps (`int`, defaults to 1000): The number of diffusion steps to train the model. beta_start (`float`, defaults to 0.0001): The starting `beta` value of inference. beta_end (`float`, defaults to 0.02): The final `beta` value. beta_schedule (`str`, defaults to `"linear"`): The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from `linear` or `scaled_linear`. trained_betas (`np.ndarray`, *optional*): Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`. prediction_type (`str`, defaults to `epsilon`, *optional*): Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process), `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
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Video](https://imagen.research.google/video/paper.pdf) paper). clip_sample (`bool`, defaults to `True`): Clip the predicted sample for numerical stability. clip_sample_range (`float`, defaults to 1.0): The maximum magnitude for sample clipping. Valid only when `clip_sample=True`. use_karras_sigmas (`bool`, *optional*, defaults to `False`): Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`, the sigmas are determined according to a sequence of noise levels {σi}. use_exponential_sigmas (`bool`, *optional*, defaults to `False`): Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process. use_beta_sigmas (`bool`, *optional*, defaults to `False`): Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
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Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information. timestep_spacing (`str`, defaults to `"linspace"`): The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information. steps_offset (`int`, defaults to 0): An offset added to the inference steps, as required by some model families. """
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_compatibles = [e.name for e in KarrasDiffusionSchedulers] order = 2
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@register_to_config def __init__( self, num_train_timesteps: int = 1000, beta_start: float = 0.00085, # sensible defaults beta_end: float = 0.012, beta_schedule: str = "linear", trained_betas: Optional[Union[np.ndarray, List[float]]] = None, prediction_type: str = "epsilon", use_karras_sigmas: Optional[bool] = False, use_exponential_sigmas: Optional[bool] = False, use_beta_sigmas: Optional[bool] = False, clip_sample: Optional[bool] = False, clip_sample_range: float = 1.0, timestep_spacing: str = "linspace", steps_offset: int = 0, ): if self.config.use_beta_sigmas and not is_scipy_available(): raise ImportError("Make sure to install scipy if you want to use beta sigmas.") if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1: raise ValueError(
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"Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used." ) if trained_betas is not None: self.betas = torch.tensor(trained_betas, dtype=torch.float32) elif beta_schedule == "linear": self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32) elif beta_schedule == "scaled_linear": # this schedule is very specific to the latent diffusion model. self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2 elif beta_schedule == "squaredcos_cap_v2": # Glide cosine schedule self.betas = betas_for_alpha_bar(num_train_timesteps, alpha_transform_type="cosine") elif beta_schedule == "exp": self.betas = betas_for_alpha_bar(num_train_timesteps, alpha_transform_type="exp") else:
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raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")
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