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# 1. Denoise model output using boundary conditions denoised = c_out * model_output + c_skip * sample if self.config.clip_denoised: denoised = denoised.clamp(-1, 1) # 2. Sample z ~ N(0, s_noise^2 * I) # Noise is not used for onestep sampling. if len(self.timesteps) > 1: noise = randn_tensor( model_output.shape, dtype=model_output.dtype, device=model_output.device, generator=generator ) else: noise = torch.zeros_like(model_output) z = noise * self.config.s_noise sigma_hat = sigma_next.clamp(min=sigma_min, max=sigma_max) # 3. Return noisy sample # tau = sigma_hat, eps = sigma_min prev_sample = denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5 # upon completion increase step index by one self._step_index += 1 if not return_dict: return (prev_sample,)
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return CMStochasticIterativeSchedulerOutput(prev_sample=prev_sample) # 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 DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin): """ `DPMSolverSinglestepScheduler` is a fast dedicated high-order solver for diffusion ODEs. 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*): Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`. solver_order (`int`, defaults to 2): The DPMSolver order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling. prediction_type (`str`, defaults to `epsilon`, *optional*):
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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): The threshold value for dynamic thresholding. Valid only when `thresholding=True` and `algorithm_type="dpmsolver++"`. algorithm_type (`str`, defaults to `dpmsolver++`):
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Algorithm type for the solver; can be `dpmsolver` or `dpmsolver++` or `sde-dpmsolver++`. The `dpmsolver` type implements the algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927) paper, and the `dpmsolver++` type implements the algorithms in the [DPMSolver++](https://huggingface.co/papers/2211.01095) paper. It is recommended to use `dpmsolver++` or `sde-dpmsolver++` with `solver_order=2` for guided sampling like in Stable Diffusion. solver_type (`str`, defaults to `midpoint`): Solver type for the second-order solver; can be `midpoint` or `heun`. The solver type slightly affects the sample quality, especially for a small number of steps. It is recommended to use `midpoint` solvers. lower_order_final (`bool`, defaults to `True`): Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
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stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10. 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 Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information. final_sigmas_type (`str`, *optional*, defaults to `"zero"`): The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final
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sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0. lambda_min_clipped (`float`, defaults to `-inf`): Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the cosine (`squaredcos_cap_v2`) noise schedule. variance_type (`str`, *optional*): Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output contains the predicted Gaussian variance. """
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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[np.ndarray] = None, solver_order: int = 2, prediction_type: str = "epsilon", thresholding: bool = False, dynamic_thresholding_ratio: float = 0.995, sample_max_value: float = 1.0, algorithm_type: str = "dpmsolver++", solver_type: str = "midpoint", lower_order_final: bool = False, use_karras_sigmas: Optional[bool] = False, use_exponential_sigmas: Optional[bool] = False, use_beta_sigmas: Optional[bool] = False, use_flow_sigmas: Optional[bool] = False, flow_shift: Optional[float] = 1.0, final_sigmas_type: Optional[str] = "zero", # "zero", "sigma_min" lambda_min_clipped: float = -float("inf"), variance_type: Optional[str] = None, ):
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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( "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used." ) if algorithm_type == "dpmsolver": deprecation_message = "algorithm_type `dpmsolver` is deprecated and will be removed in a future version. Choose from `dpmsolver++` or `sde-dpmsolver++` instead" deprecate("algorithm_types=dpmsolver", "1.0.0", deprecation_message)
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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) else: raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")
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self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) # Currently we only support VP-type noise schedule self.alpha_t = torch.sqrt(self.alphas_cumprod) self.sigma_t = torch.sqrt(1 - self.alphas_cumprod) self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t) self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 # standard deviation of the initial noise distribution self.init_noise_sigma = 1.0
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# settings for DPM-Solver if algorithm_type not in ["dpmsolver", "dpmsolver++", "sde-dpmsolver++"]: if algorithm_type == "deis": self.register_to_config(algorithm_type="dpmsolver++") else: raise NotImplementedError(f"{algorithm_type} is not implemented for {self.__class__}") 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__}") if algorithm_type not in ["dpmsolver++", "sde-dpmsolver++"] and final_sigmas_type == "zero": raise ValueError( f"`final_sigmas_type` {final_sigmas_type} is not supported for `algorithm_type` {algorithm_type}. Please chooose `sigma_min` instead." )
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# setable values self.num_inference_steps = None timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy() self.timesteps = torch.from_numpy(timesteps) self.model_outputs = [None] * solver_order self.sample = None self.order_list = self.get_order_list(num_train_timesteps) self._step_index = None self._begin_index = None self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication def get_order_list(self, num_inference_steps: int) -> List[int]: """ Computes the solver order at each time step.
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Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. """ steps = num_inference_steps order = self.config.solver_order if order > 3: raise ValueError("Order > 3 is not supported by this scheduler") if self.config.lower_order_final: if order == 3: if steps % 3 == 0: orders = [1, 2, 3] * (steps // 3 - 1) + [1, 2] + [1] elif steps % 3 == 1: orders = [1, 2, 3] * (steps // 3) + [1] else: orders = [1, 2, 3] * (steps // 3) + [1, 2] elif order == 2: if steps % 2 == 0: orders = [1, 2] * (steps // 2 - 1) + [1, 1] else: orders = [1, 2] * (steps // 2) + [1] elif order == 1: orders = [1] * steps else: if order == 3:
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orders = [1, 2, 3] * (steps // 3) elif order == 2: orders = [1, 2] * (steps // 2) elif order == 1: orders = [1] * steps
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if self.config.final_sigmas_type == "zero": orders[-1] = 1 return orders @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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def set_timesteps( self, num_inference_steps: 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. 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 schedule is used. If `timesteps` is passed, `num_inference_steps` must be `None`. """ if num_inference_steps is None and timesteps is None: raise ValueError("Must pass exactly one of `num_inference_steps` or `timesteps`.") if num_inference_steps is not None and timesteps is not None: raise ValueError("Must pass exactly one of `num_inference_steps` or `timesteps`.")
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if timesteps is not None and self.config.use_karras_sigmas: raise ValueError("Cannot use `timesteps` when `config.use_karras_sigmas=True`.") if timesteps is not None and self.config.use_exponential_sigmas: raise ValueError("Cannot set `timesteps` with `config.use_exponential_sigmas = True`.") if timesteps is not None and self.config.use_beta_sigmas: raise ValueError("Cannot set `timesteps` with `config.use_beta_sigmas = True`.")
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num_inference_steps = num_inference_steps or len(timesteps) self.num_inference_steps = num_inference_steps if timesteps is not None: timesteps = np.array(timesteps).astype(np.int64) else: # Clipping the minimum of all lambda(t) for numerical stability. # This is critical for cosine (squaredcos_cap_v2) noise schedule. clipped_idx = torch.searchsorted(torch.flip(self.lambda_t, [0]), self.config.lambda_min_clipped) clipped_idx = clipped_idx.item() timesteps = ( np.linspace(0, self.config.num_train_timesteps - 1 - clipped_idx, num_inference_steps + 1) .round()[::-1][:-1] .copy() .astype(np.int64) )
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sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) log_sigmas = np.log(sigmas) if self.config.use_karras_sigmas: sigmas = np.flip(sigmas).copy() sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round() elif self.config.use_exponential_sigmas: sigmas = np.flip(sigmas).copy() sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=num_inference_steps) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]) elif self.config.use_beta_sigmas: sigmas = np.flip(sigmas).copy() sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=num_inference_steps) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
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elif self.config.use_flow_sigmas: alphas = np.linspace(1, 1 / self.config.num_train_timesteps, num_inference_steps + 1) sigmas = 1.0 - alphas sigmas = np.flip(self.config.flow_shift * sigmas / (1 + (self.config.flow_shift - 1) * sigmas))[:-1].copy() timesteps = (sigmas * self.config.num_train_timesteps).copy() else: sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
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if self.config.final_sigmas_type == "sigma_min": sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5 elif self.config.final_sigmas_type == "zero": sigma_last = 0 else: raise ValueError( f" `final_sigmas_type` must be one of `sigma_min` or `zero`, but got {self.config.final_sigmas_type}" ) sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32) self.sigmas = torch.from_numpy(sigmas).to(device=device) self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64) self.model_outputs = [None] * self.config.solver_order self.sample = None
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if not self.config.lower_order_final and num_inference_steps % self.config.solver_order != 0: logger.warning( "Changing scheduler {self.config} to have `lower_order_final` set to True to handle uneven amount of inference steps. Please make sure to always use an even number of `num_inference steps when using `lower_order_final=False`." ) self.register_to_config(lower_order_final=True) if not self.config.lower_order_final and self.config.final_sigmas_type == "zero": logger.warning( " `last_sigmas_type='zero'` is not supported for `lower_order_final=False`. Changing scheduler {self.config} to have `lower_order_final` set to True." ) self.register_to_config(lower_order_final=True) self.order_list = self.get_order_list(num_inference_steps)
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# 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 # 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."
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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 # 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"
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sample = sample.reshape(batch_size, channels, *remaining_dims) sample = sample.to(dtype) return sample # 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) # transform interpolation to time range t = (1 - w) * low_idx + w * high_idx t = t.reshape(sigma.shape) return t
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# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._sigma_to_alpha_sigma_t def _sigma_to_alpha_sigma_t(self, sigma): if self.config.use_flow_sigmas: alpha_t = 1 - sigma sigma_t = sigma else: alpha_t = 1 / ((sigma**2 + 1) ** 0.5) sigma_t = sigma * alpha_t return alpha_t, sigma_t # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor: """Constructs the noise schedule of Karras et al. (2022).""" # Hack to make sure that other schedulers which copy this function don't break # TODO: Add this logic to the other schedulers if hasattr(self.config, "sigma_min"): sigma_min = self.config.sigma_min else: sigma_min = None
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if hasattr(self.config, "sigma_max"): sigma_max = self.config.sigma_max else: sigma_max = None sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item() sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item() rho = 7.0 # 7.0 is the value used in the paper ramp = np.linspace(0, 1, num_inference_steps) 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_euler_discrete.EulerDiscreteScheduler._convert_to_exponential def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor: """Constructs an exponential noise schedule."""
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# Hack to make sure that other schedulers which copy this function don't break # TODO: Add this logic to the other schedulers if hasattr(self.config, "sigma_min"): sigma_min = self.config.sigma_min else: sigma_min = None if hasattr(self.config, "sigma_max"): sigma_max = self.config.sigma_max else: sigma_max = None sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item() sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item() sigmas = np.exp(np.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps)) return sigmas
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# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta def _convert_to_beta( self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6 ) -> torch.Tensor: """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)""" # Hack to make sure that other schedulers which copy this function don't break # TODO: Add this logic to the other schedulers if hasattr(self.config, "sigma_min"): sigma_min = self.config.sigma_min else: sigma_min = None if hasattr(self.config, "sigma_max"): sigma_max = self.config.sigma_max else: sigma_max = None sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item() sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
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sigmas = np.array( [ sigma_min + (ppf * (sigma_max - sigma_min)) for ppf in [ scipy.stats.beta.ppf(timestep, alpha, beta) for timestep in 1 - np.linspace(0, 1, num_inference_steps) ] ] ) return sigmas def convert_model_output( self, model_output: torch.Tensor, *args, sample: torch.Tensor = None, **kwargs, ) -> 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.
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Returns: `torch.Tensor`: The converted model output. """ timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None) if sample is None: if len(args) > 1: sample = args[1] else: raise ValueError("missing `sample` as a required keyward argument") if timestep is not None: deprecate( "timesteps", "1.0.0", "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", ) # DPM-Solver++ needs to solve an integral of the data prediction model. if self.config.algorithm_type in ["dpmsolver++", "sde-dpmsolver++"]: if self.config.prediction_type == "epsilon": # DPM-Solver and DPM-Solver++ only need the "mean" output. if self.config.variance_type in ["learned", "learned_range"]:
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model_output = model_output[:, :3] sigma = self.sigmas[self.step_index] alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma) x0_pred = (sample - sigma_t * model_output) / alpha_t elif self.config.prediction_type == "sample": x0_pred = model_output elif self.config.prediction_type == "v_prediction": sigma = self.sigmas[self.step_index] alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma) x0_pred = alpha_t * sample - sigma_t * model_output elif self.config.prediction_type == "flow_prediction": sigma_t = self.sigmas[self.step_index] x0_pred = sample - sigma_t * model_output else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, "
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"`v_prediction`, or `flow_prediction` for the DPMSolverSinglestepScheduler." )
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if self.config.thresholding: x0_pred = self._threshold_sample(x0_pred) return x0_pred
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# DPM-Solver needs to solve an integral of the noise prediction model. elif self.config.algorithm_type == "dpmsolver": if self.config.prediction_type == "epsilon": # DPM-Solver and DPM-Solver++ only need the "mean" output. if self.config.variance_type in ["learned", "learned_range"]: epsilon = model_output[:, :3] else: epsilon = model_output elif self.config.prediction_type == "sample": sigma = self.sigmas[self.step_index] alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma) epsilon = (sample - alpha_t * model_output) / sigma_t elif self.config.prediction_type == "v_prediction": sigma = self.sigmas[self.step_index] alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma) epsilon = alpha_t * model_output + sigma_t * sample else: raise ValueError(
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f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" " `v_prediction` for the DPMSolverSinglestepScheduler." )
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if self.config.thresholding: alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep] x0_pred = (sample - sigma_t * epsilon) / alpha_t x0_pred = self._threshold_sample(x0_pred) epsilon = (sample - alpha_t * x0_pred) / sigma_t return epsilon def dpm_solver_first_order_update( self, model_output: torch.Tensor, *args, sample: torch.Tensor = None, noise: Optional[torch.Tensor] = None, **kwargs, ) -> torch.Tensor: """ One step for the first-order DPMSolver (equivalent to DDIM).
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Args: model_output (`torch.Tensor`): The direct output from the learned diffusion model. timestep (`int`): The current discrete timestep in the diffusion chain. prev_timestep (`int`): The previous discrete timestep in the diffusion chain. 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. """ timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None) prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None) if sample is None: if len(args) > 2: sample = args[2] else: raise ValueError(" missing `sample` as a required keyward argument") if timestep is not None: deprecate( "timesteps", "1.0.0", "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", )
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if prev_timestep is not None: deprecate( "prev_timestep", "1.0.0", "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", ) 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 if self.config.algorithm_type == "dpmsolver++": x_t = (sigma_t / sigma_s) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * model_output elif self.config.algorithm_type == "dpmsolver": x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
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elif self.config.algorithm_type == "sde-dpmsolver++": 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 singlestep_dpm_solver_second_order_update( self, model_output_list: List[torch.Tensor], *args, sample: torch.Tensor = None, noise: Optional[torch.Tensor] = None, **kwargs, ) -> torch.Tensor: """ One step for the second-order singlestep DPMSolver that computes the solution at time `prev_timestep` from the time `timestep_list[-2]`. Args: model_output_list (`List[torch.Tensor]`): The direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): The current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): The previous discrete timestep in the diffusion chain. 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. """ timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None) prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None) if sample is None: if len(args) > 2: sample = args[2] else: raise ValueError(" missing `sample` as a required keyward argument") if timestep_list is not None: deprecate( "timestep_list", "1.0.0", "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", )
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if prev_timestep is not None: deprecate( "prev_timestep", "1.0.0", "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", ) sigma_t, sigma_s0, sigma_s1 = ( self.sigmas[self.step_index + 1], self.sigmas[self.step_index], self.sigmas[self.step_index - 1], ) 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]
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h, h_0 = lambda_t - lambda_s1, lambda_s0 - lambda_s1 r0 = h_0 / h D0, D1 = m1, (1.0 / r0) * (m0 - m1) if self.config.algorithm_type == "dpmsolver++": # See https://arxiv.org/abs/2211.01095 for detailed derivations if self.config.solver_type == "midpoint": x_t = ( (sigma_t / sigma_s1) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * D0 - 0.5 * (alpha_t * (torch.exp(-h) - 1.0)) * D1 ) elif self.config.solver_type == "heun": x_t = ( (sigma_t / sigma_s1) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * D0 + (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1 ) elif self.config.algorithm_type == "dpmsolver": # See https://arxiv.org/abs/2206.00927 for detailed derivations if self.config.solver_type == "midpoint": x_t = (
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(alpha_t / alpha_s1) * sample - (sigma_t * (torch.exp(h) - 1.0)) * D0 - 0.5 * (sigma_t * (torch.exp(h) - 1.0)) * D1 ) elif self.config.solver_type == "heun": x_t = ( (alpha_t / alpha_s1) * sample - (sigma_t * (torch.exp(h) - 1.0)) * D0 - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1 ) elif self.config.algorithm_type == "sde-dpmsolver++": assert noise is not None if self.config.solver_type == "midpoint": x_t = ( (sigma_t / sigma_s1 * 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 = (
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(sigma_t / sigma_s1 * 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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def singlestep_dpm_solver_third_order_update( self, model_output_list: List[torch.Tensor], *args, sample: torch.Tensor = None, noise: Optional[torch.Tensor] = None, **kwargs, ) -> torch.Tensor: """ One step for the third-order singlestep DPMSolver that computes the solution at time `prev_timestep` from the time `timestep_list[-3]`. Args: model_output_list (`List[torch.Tensor]`): The direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): The current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): The previous discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by diffusion process.
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Returns: `torch.Tensor`: The sample tensor at the previous timestep. """ timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None) prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None) if sample is None: if len(args) > 2: sample = args[2] else: raise ValueError(" missing`sample` as a required keyward argument") if timestep_list is not None: deprecate( "timestep_list", "1.0.0", "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", )
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if prev_timestep is not None: deprecate( "prev_timestep", "1.0.0", "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", ) sigma_t, sigma_s0, sigma_s1, sigma_s2 = ( self.sigmas[self.step_index + 1], self.sigmas[self.step_index], self.sigmas[self.step_index - 1], self.sigmas[self.step_index - 2], ) 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) alpha_s2, sigma_s2 = self._sigma_to_alpha_sigma_t(sigma_s2)
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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) lambda_s2 = torch.log(alpha_s2) - torch.log(sigma_s2) m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
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h, h_0, h_1 = lambda_t - lambda_s2, lambda_s0 - lambda_s2, lambda_s1 - lambda_s2 r0, r1 = h_0 / h, h_1 / h D0 = m2 D1_0, D1_1 = (1.0 / r1) * (m1 - m2), (1.0 / r0) * (m0 - m2) D1 = (r0 * D1_0 - r1 * D1_1) / (r0 - r1) D2 = 2.0 * (D1_1 - D1_0) / (r0 - r1) if self.config.algorithm_type == "dpmsolver++": # See https://arxiv.org/abs/2206.00927 for detailed derivations if self.config.solver_type == "midpoint": x_t = ( (sigma_t / sigma_s2) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * D0 + (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1_1 ) elif self.config.solver_type == "heun": x_t = ( (sigma_t / sigma_s2) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * D0 + (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1
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- (alpha_t * ((torch.exp(-h) - 1.0 + h) / h**2 - 0.5)) * D2 ) elif self.config.algorithm_type == "dpmsolver": # See https://arxiv.org/abs/2206.00927 for detailed derivations if self.config.solver_type == "midpoint": x_t = ( (alpha_t / alpha_s2) * sample - (sigma_t * (torch.exp(h) - 1.0)) * D0 - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1_1 ) elif self.config.solver_type == "heun": x_t = ( (alpha_t / alpha_s2) * sample - (sigma_t * (torch.exp(h) - 1.0)) * D0 - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1 - (sigma_t * ((torch.exp(h) - 1.0 - h) / h**2 - 0.5)) * D2 ) elif self.config.algorithm_type == "sde-dpmsolver++": assert noise is not None if self.config.solver_type == "midpoint":
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x_t = ( (sigma_t / sigma_s2 * torch.exp(-h)) * sample + (alpha_t * (1.0 - torch.exp(-2.0 * h))) * D0 + (alpha_t * ((1.0 - torch.exp(-2.0 * h)) / (-2.0 * h) + 1.0)) * D1_1 + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise ) elif self.config.solver_type == "heun": x_t = ( (sigma_t / sigma_s2 * torch.exp(-h)) * sample + (alpha_t * (1.0 - torch.exp(-2.0 * h))) * D0 + (alpha_t * ((1.0 - torch.exp(-2.0 * h)) / (-2.0 * h) + 1.0)) * D1 + (alpha_t * ((1.0 - torch.exp(-2.0 * h) + (-2.0 * h)) / (-2.0 * h) ** 2 - 0.5)) * D2 + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise ) return x_t
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def singlestep_dpm_solver_update( self, model_output_list: List[torch.Tensor], *args, sample: torch.Tensor = None, order: int = None, noise: Optional[torch.Tensor] = None, **kwargs, ) -> torch.Tensor: """ One step for the singlestep DPMSolver. Args: model_output_list (`List[torch.Tensor]`): The direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): The current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): The previous discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by diffusion process. order (`int`): The solver order at this step.
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Returns: `torch.Tensor`: The sample tensor at the previous timestep. """ timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None) prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None) if sample is None: if len(args) > 2: sample = args[2] else: raise ValueError(" missing`sample` as a required keyward argument") if order is None: if len(args) > 3: order = args[3] else: raise ValueError(" missing `order` as a required keyward argument") if timestep_list is not None: deprecate( "timestep_list", "1.0.0", "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", )
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if prev_timestep is not None: deprecate( "prev_timestep", "1.0.0", "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", ) if order == 1: return self.dpm_solver_first_order_update(model_output_list[-1], sample=sample, noise=noise) elif order == 2: return self.singlestep_dpm_solver_second_order_update(model_output_list, sample=sample, noise=noise) elif order == 3: return self.singlestep_dpm_solver_third_order_update(model_output_list, sample=sample, noise=noise) else: raise ValueError(f"Order must be 1, 2, 3, got {order}")
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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 singlestep 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. 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. """ 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" )
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if self.step_index is None: self._init_step_index(timestep) 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.config.algorithm_type == "sde-dpmsolver++": noise = randn_tensor( model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype ) else: noise = None order = self.order_list[self.step_index] # For img2img denoising might start with order>1 which is not possible # In this case make sure that the first two steps are both order=1 while self.model_outputs[-order] is None: order -= 1 # For single-step solvers, we use the initial value at each time with order = 1. if order == 1: self.sample = sample
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prev_sample = self.singlestep_dpm_solver_update( self.model_outputs, sample=self.sample, order=order, noise=noise ) # upon completion increase step index by one, noise=noise self._step_index += 1 if not return_dict: return (prev_sample,) return SchedulerOutput(prev_sample=prev_sample) def scale_model_input(self, sample: torch.Tensor, *args, **kwargs) -> 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. Returns: `torch.Tensor`: A scaled input sample. """ return sample
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# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise def add_noise( self, original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor, ) -> 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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# begin_index is None when the 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) alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma) noisy_samples = alpha_t * original_samples + sigma_t * noise return noisy_samples def __len__(self): return self.config.num_train_timesteps
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class DDIMSchedulerState: common: CommonSchedulerState final_alpha_cumprod: jnp.ndarray # setable values init_noise_sigma: jnp.ndarray timesteps: jnp.ndarray num_inference_steps: Optional[int] = None @classmethod def create( cls, common: CommonSchedulerState, final_alpha_cumprod: jnp.ndarray, init_noise_sigma: jnp.ndarray, timesteps: jnp.ndarray, ): return cls( common=common, final_alpha_cumprod=final_alpha_cumprod, init_noise_sigma=init_noise_sigma, timesteps=timesteps, )
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class FlaxDDIMSchedulerOutput(FlaxSchedulerOutput): state: DDIMSchedulerState
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class FlaxDDIMScheduler(FlaxSchedulerMixin, ConfigMixin): """ Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising diffusion probabilistic models (DDPMs) with non-Markovian guidance. [`~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. For more details, see the original paper: https://arxiv.org/abs/2010.02502
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Args: num_train_timesteps (`int`): number of diffusion steps used to train the model. beta_start (`float`): the starting `beta` value of inference. beta_end (`float`): the final `beta` value. beta_schedule (`str`): 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 (`jnp.ndarray`, optional): option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc. clip_sample (`bool`, default `True`): option to clip predicted sample between for numerical stability. The clip range is determined by `clip_sample_range`. clip_sample_range (`float`, default `1.0`): the maximum magnitude for sample clipping. Valid only when `clip_sample=True`. set_alpha_to_one (`bool`, default `True`):
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each diffusion step uses the value of alphas product 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 value of alpha at step 0. steps_offset (`int`, default `0`): An offset added to the inference steps, as required by some model families. prediction_type (`str`, default `epsilon`): indicates whether the model predicts the noise (epsilon), or the samples. One of `epsilon`, `sample`. `v-prediction` is not supported for this scheduler. dtype (`jnp.dtype`, *optional*, defaults to `jnp.float32`): the `dtype` used for params and computation. """
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_compatibles = [e.name for e in FlaxKarrasDiffusionSchedulers] dtype: jnp.dtype @property def has_state(self): return True @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[jnp.ndarray] = None, clip_sample: bool = True, clip_sample_range: float = 1.0, set_alpha_to_one: bool = True, steps_offset: int = 0, prediction_type: str = "epsilon", dtype: jnp.dtype = jnp.float32, ): self.dtype = dtype def create_state(self, common: Optional[CommonSchedulerState] = None) -> DDIMSchedulerState: if common is None: common = CommonSchedulerState.create(self)
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# 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. final_alpha_cumprod = ( jnp.array(1.0, dtype=self.dtype) if self.config.set_alpha_to_one else common.alphas_cumprod[0] ) # standard deviation of the initial noise distribution init_noise_sigma = jnp.array(1.0, dtype=self.dtype) timesteps = jnp.arange(0, self.config.num_train_timesteps).round()[::-1] return DDIMSchedulerState.create( common=common, final_alpha_cumprod=final_alpha_cumprod, init_noise_sigma=init_noise_sigma, timesteps=timesteps, )
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def scale_model_input( self, state: DDIMSchedulerState, sample: jnp.ndarray, timestep: Optional[int] = None ) -> jnp.ndarray: """ Args: state (`PNDMSchedulerState`): the `FlaxPNDMScheduler` state data class instance. sample (`jnp.ndarray`): input sample timestep (`int`, optional): current timestep Returns: `jnp.ndarray`: scaled input sample """ return sample def set_timesteps( self, state: DDIMSchedulerState, num_inference_steps: int, shape: Tuple = () ) -> DDIMSchedulerState: """ Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
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Args: state (`DDIMSchedulerState`): the `FlaxDDIMScheduler` state data class instance. num_inference_steps (`int`): the number of diffusion steps used when generating samples with a pre-trained model. """ step_ratio = self.config.num_train_timesteps // num_inference_steps # creates integer timesteps by multiplying by ratio # rounding to avoid issues when num_inference_step is power of 3 timesteps = (jnp.arange(0, num_inference_steps) * step_ratio).round()[::-1] + self.config.steps_offset return state.replace( num_inference_steps=num_inference_steps, timesteps=timesteps, )
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def _get_variance(self, state: DDIMSchedulerState, timestep, prev_timestep): alpha_prod_t = state.common.alphas_cumprod[timestep] alpha_prod_t_prev = jnp.where( prev_timestep >= 0, state.common.alphas_cumprod[prev_timestep], state.final_alpha_cumprod ) beta_prod_t = 1 - alpha_prod_t beta_prod_t_prev = 1 - alpha_prod_t_prev variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev) return variance def step( self, state: DDIMSchedulerState, model_output: jnp.ndarray, timestep: int, sample: jnp.ndarray, eta: float = 0.0, return_dict: bool = True, ) -> Union[FlaxDDIMSchedulerOutput, Tuple]: """ Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion process from the learned model outputs (most often the predicted noise).
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Args: state (`DDIMSchedulerState`): the `FlaxDDIMScheduler` state data class instance. model_output (`jnp.ndarray`): direct output from learned diffusion model. timestep (`int`): current discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process. return_dict (`bool`): option for returning tuple rather than FlaxDDIMSchedulerOutput class Returns: [`FlaxDDIMSchedulerOutput`] or `tuple`: [`FlaxDDIMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor. """ if state.num_inference_steps is None: raise ValueError( "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" )
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# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf # Ideally, read DDIM paper in-detail understanding # Notation (<variable name> -> <name in paper> # - pred_noise_t -> e_theta(x_t, t) # - pred_original_sample -> f_theta(x_t, t) or x_0 # - std_dev_t -> sigma_t # - eta -> η # - pred_sample_direction -> "direction pointing to x_t" # - pred_prev_sample -> "x_t-1" # 1. get previous step value (=t-1) prev_timestep = timestep - self.config.num_train_timesteps // state.num_inference_steps alphas_cumprod = state.common.alphas_cumprod final_alpha_cumprod = state.final_alpha_cumprod # 2. compute alphas, betas alpha_prod_t = alphas_cumprod[timestep] alpha_prod_t_prev = jnp.where(prev_timestep >= 0, alphas_cumprod[prev_timestep], final_alpha_cumprod) beta_prod_t = 1 - alpha_prod_t
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# 3. compute predicted original sample from predicted noise also called # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf if self.config.prediction_type == "epsilon": pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5) pred_epsilon = model_output elif self.config.prediction_type == "sample": pred_original_sample = model_output pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5) elif self.config.prediction_type == "v_prediction": pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" " `v_prediction`"
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)
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# 4. Clip or threshold "predicted x_0" if self.config.clip_sample: pred_original_sample = pred_original_sample.clip( -self.config.clip_sample_range, self.config.clip_sample_range ) # 4. compute variance: "sigma_t(η)" -> see formula (16) # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1) variance = self._get_variance(state, timestep, prev_timestep) std_dev_t = eta * variance ** (0.5) # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction if not return_dict: return (prev_sample, state)
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return FlaxDDIMSchedulerOutput(prev_sample=prev_sample, state=state) def add_noise( self, state: DDIMSchedulerState, original_samples: jnp.ndarray, noise: jnp.ndarray, timesteps: jnp.ndarray, ) -> jnp.ndarray: return add_noise_common(state.common, original_samples, noise, timesteps) def get_velocity( self, state: DDIMSchedulerState, sample: jnp.ndarray, noise: jnp.ndarray, timesteps: jnp.ndarray, ) -> jnp.ndarray: return get_velocity_common(state.common, sample, noise, timesteps) def __len__(self): return self.config.num_train_timesteps
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class DPMSolverMultistepSchedulerState: common: CommonSchedulerState alpha_t: jnp.ndarray sigma_t: jnp.ndarray lambda_t: jnp.ndarray # setable values init_noise_sigma: jnp.ndarray timesteps: jnp.ndarray num_inference_steps: Optional[int] = None # running values model_outputs: Optional[jnp.ndarray] = None lower_order_nums: Optional[jnp.int32] = None prev_timestep: Optional[jnp.int32] = None cur_sample: Optional[jnp.ndarray] = None @classmethod def create( cls, common: CommonSchedulerState, alpha_t: jnp.ndarray, sigma_t: jnp.ndarray, lambda_t: jnp.ndarray, init_noise_sigma: jnp.ndarray, timesteps: jnp.ndarray, ): return cls( common=common, alpha_t=alpha_t, sigma_t=sigma_t, lambda_t=lambda_t, init_noise_sigma=init_noise_sigma, timesteps=timesteps, )
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class FlaxDPMSolverMultistepSchedulerOutput(FlaxSchedulerOutput): state: DPMSolverMultistepSchedulerState
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class FlaxDPMSolverMultistepScheduler(FlaxSchedulerMixin, ConfigMixin): """ DPM-Solver (and the improved version DPM-Solver++) is a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. Empirically, sampling by DPM-Solver with only 20 steps can generate high-quality samples, and it can generate quite good samples even in only 10 steps. For more details, see the original paper: https://arxiv.org/abs/2206.00927 and https://arxiv.org/abs/2211.01095 Currently, we support the multistep DPM-Solver for both noise prediction models and data prediction models. We recommend to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling.
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We also support the "dynamic thresholding" method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space diffusion models, you can set both `algorithm_type="dpmsolver++"` and `thresholding=True` to use the dynamic thresholding. Note that the thresholding method is unsuitable for latent-space diffusion models (such as stable-diffusion). [`~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. For more details, see the original paper: https://arxiv.org/abs/2206.00927 and https://arxiv.org/abs/2211.01095
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Args: num_train_timesteps (`int`): number of diffusion steps used to train the model. beta_start (`float`): the starting `beta` value of inference. beta_end (`float`): the final `beta` value. beta_schedule (`str`): 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): option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc. solver_order (`int`, default `2`): the order of DPM-Solver; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling. prediction_type (`str`, default `epsilon`): indicates whether the model predicts the noise (epsilon), or the data / `x0`. One of `epsilon`, `sample`, or `v-prediction`.
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thresholding (`bool`, default `False`): whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487). For pixel-space diffusion models, you can set both `algorithm_type=dpmsolver++` and `thresholding=True` to use the dynamic thresholding. Note that the thresholding method is unsuitable for latent-space diffusion models (such as stable-diffusion). dynamic_thresholding_ratio (`float`, default `0.995`): the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen (https://arxiv.org/abs/2205.11487). sample_max_value (`float`, default `1.0`): the threshold value for dynamic thresholding. Valid only when `thresholding=True` and `algorithm_type="dpmsolver++`. algorithm_type (`str`, default `dpmsolver++`):
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the algorithm type for the solver. Either `dpmsolver` or `dpmsolver++`. The `dpmsolver` type implements the algorithms in https://arxiv.org/abs/2206.00927, and the `dpmsolver++` type implements the algorithms in https://arxiv.org/abs/2211.01095. We recommend to use `dpmsolver++` with `solver_order=2` for guided sampling (e.g. stable-diffusion). solver_type (`str`, default `midpoint`): the solver type for the second-order solver. Either `midpoint` or `heun`. The solver type slightly affects the sample quality, especially for small number of steps. We empirically find that `midpoint` solvers are slightly better, so we recommend to use the `midpoint` type. lower_order_final (`bool`, default `True`): whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. We empirically
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find this trick can stabilize the sampling of DPM-Solver for steps < 15, especially for steps <= 10. 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. dtype (`jnp.dtype`, *optional*, defaults to `jnp.float32`): the `dtype` used for params and computation. """
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_compatibles = [e.name for e in FlaxKarrasDiffusionSchedulers] dtype: jnp.dtype @property def has_state(self): return True @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[jnp.ndarray] = None, solver_order: int = 2, prediction_type: str = "epsilon", thresholding: bool = False, dynamic_thresholding_ratio: float = 0.995, sample_max_value: float = 1.0, algorithm_type: str = "dpmsolver++", solver_type: str = "midpoint", lower_order_final: bool = True, timestep_spacing: str = "linspace", dtype: jnp.dtype = jnp.float32, ): self.dtype = dtype
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def create_state(self, common: Optional[CommonSchedulerState] = None) -> DPMSolverMultistepSchedulerState: if common is None: common = CommonSchedulerState.create(self) # Currently we only support VP-type noise schedule alpha_t = jnp.sqrt(common.alphas_cumprod) sigma_t = jnp.sqrt(1 - common.alphas_cumprod) lambda_t = jnp.log(alpha_t) - jnp.log(sigma_t) # settings for DPM-Solver if self.config.algorithm_type not in ["dpmsolver", "dpmsolver++"]: raise NotImplementedError(f"{self.config.algorithm_type} is not implemented for {self.__class__}") if self.config.solver_type not in ["midpoint", "heun"]: raise NotImplementedError(f"{self.config.solver_type} is not implemented for {self.__class__}") # standard deviation of the initial noise distribution init_noise_sigma = jnp.array(1.0, dtype=self.dtype) timesteps = jnp.arange(0, self.config.num_train_timesteps).round()[::-1]
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return DPMSolverMultistepSchedulerState.create( common=common, alpha_t=alpha_t, sigma_t=sigma_t, lambda_t=lambda_t, init_noise_sigma=init_noise_sigma, timesteps=timesteps, ) def set_timesteps( self, state: DPMSolverMultistepSchedulerState, num_inference_steps: int, shape: Tuple ) -> DPMSolverMultistepSchedulerState: """ Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
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Args: state (`DPMSolverMultistepSchedulerState`): the `FlaxDPMSolverMultistepScheduler` state data class instance. num_inference_steps (`int`): the number of diffusion steps used when generating samples with a pre-trained model. shape (`Tuple`): the shape of the samples to be generated. """ last_timestep = self.config.num_train_timesteps if self.config.timestep_spacing == "linspace": timesteps = ( jnp.linspace(0, last_timestep - 1, num_inference_steps + 1).round()[::-1][:-1].astype(jnp.int32) ) elif self.config.timestep_spacing == "leading": step_ratio = last_timestep // (num_inference_steps + 1) # creates integer timesteps by multiplying by ratio # casting to int to avoid issues when num_inference_step is power of 3 timesteps = (
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(jnp.arange(0, num_inference_steps + 1) * step_ratio).round()[::-1][:-1].copy().astype(jnp.int32) ) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = self.config.num_train_timesteps / 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 = jnp.arange(last_timestep, 0, -step_ratio).round().copy().astype(jnp.int32) 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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# initial running values model_outputs = jnp.zeros((self.config.solver_order,) + shape, dtype=self.dtype) lower_order_nums = jnp.int32(0) prev_timestep = jnp.int32(-1) cur_sample = jnp.zeros(shape, dtype=self.dtype) return state.replace( num_inference_steps=num_inference_steps, timesteps=timesteps, model_outputs=model_outputs, lower_order_nums=lower_order_nums, prev_timestep=prev_timestep, cur_sample=cur_sample, ) def convert_model_output( self, state: DPMSolverMultistepSchedulerState, model_output: jnp.ndarray, timestep: int, sample: jnp.ndarray, ) -> jnp.ndarray: """ Convert the model output to the corresponding type that the algorithm (DPM-Solver / DPM-Solver++) needs.
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