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self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) # set all values self.set_timesteps(num_train_timesteps, None, num_train_timesteps) self.use_karras_sigmas = use_karras_sigmas 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_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()
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# 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() @property def init_noise_sigma(self): # standard deviation of the initial noise distribution if self.config.timestep_spacing in ["linspace", "trailing"]: return self.sigmas.max() return (self.sigmas.max() ** 2 + 1) ** 0.5 @property def step_index(self): """ The index counter for current timestep. It will increase 1 after each scheduler step. """ return self._step_index
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@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 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.
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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 = sample / ((sigma**2 + 1) ** 0.5) return sample def set_timesteps( self, num_inference_steps: Optional[int] = None, device: Union[str, torch.device] = None, num_train_timesteps: Optional[int] = 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. num_train_timesteps (`int`, *optional*): The number of diffusion steps used when training the model. If `None`, the default `num_train_timesteps` attribute is used. timesteps (`List[int]`, *optional*): Custom timesteps used to support arbitrary spacing between timesteps. If `None`, timesteps will be generated based on the `timestep_spacing` attribute. If `timesteps` is passed, `num_inference_steps` must be `None`, and `timestep_spacing` attribute will be ignored. """ if num_inference_steps is None and timesteps is None:
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raise ValueError("Must pass exactly one of `num_inference_steps` or `custom_timesteps`.") 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`.") if timesteps is not None and self.config.use_karras_sigmas: raise ValueError("Cannot use `timesteps` with `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 num_train_timesteps = num_train_timesteps or self.config.num_train_timesteps
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if timesteps is not None: timesteps = np.array(timesteps, dtype=np.float32) else: # "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, num_train_timesteps - 1, num_inference_steps, dtype=np.float32)[::-1].copy() elif self.config.timestep_spacing == "leading": step_ratio = 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.float32) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = num_train_timesteps / self.num_inference_steps
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# creates integer timesteps by multiplying by ratio # casting to int to avoid issues when num_inference_step is power of 3 timesteps = (np.arange(num_train_timesteps, 0, -step_ratio)).round().copy().astype(np.float32) 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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sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) log_sigmas = np.log(sigmas) sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas) if self.config.use_karras_sigmas: sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]) elif self.config.use_exponential_sigmas: 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 = 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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sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32) sigmas = torch.from_numpy(sigmas).to(device=device) self.sigmas = torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2), sigmas[-1:]]) timesteps = torch.from_numpy(timesteps) timesteps = torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2)]) self.timesteps = timesteps.to(device=device, dtype=torch.float32) # empty dt and derivative self.prev_derivative = None self.dt = None 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_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]
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# 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 # 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)."""
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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() 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
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# 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.""" # 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 @property def state_in_first_order(self): return self.dt is None # 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
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def step( self, model_output: Union[torch.Tensor, np.ndarray], timestep: Union[float, torch.Tensor], sample: Union[torch.Tensor, np.ndarray], return_dict: bool = True, ) -> Union[HeunDiscreteSchedulerOutput, 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). 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. return_dict (`bool`): Whether or not to return a [`~schedulers.scheduling_heun_discrete.HeunDiscreteSchedulerOutput`] or tuple.
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Returns: [`~schedulers.scheduling_heun_discrete.HeunDiscreteSchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_heun_discrete.HeunDiscreteSchedulerOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor. """ if self.step_index is None: self._init_step_index(timestep) if self.state_in_first_order: sigma = self.sigmas[self.step_index] sigma_next = self.sigmas[self.step_index + 1] else: # 2nd order / Heun's method sigma = self.sigmas[self.step_index - 1] sigma_next = self.sigmas[self.step_index]
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# currently only gamma=0 is supported. This usually works best anyways. # We can support gamma in the future but then need to scale the timestep before # passing it to the model which requires a change in API gamma = 0 sigma_hat = sigma * (gamma + 1) # Note: sigma_hat == sigma for now
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# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise if self.config.prediction_type == "epsilon": sigma_input = sigma_hat if self.state_in_first_order else sigma_next pred_original_sample = sample - sigma_input * model_output elif self.config.prediction_type == "v_prediction": sigma_input = sigma_hat if self.state_in_first_order else sigma_next pred_original_sample = model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + ( sample / (sigma_input**2 + 1) ) elif self.config.prediction_type == "sample": pred_original_sample = model_output else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`" )
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if self.config.clip_sample: pred_original_sample = pred_original_sample.clamp( -self.config.clip_sample_range, self.config.clip_sample_range ) if self.state_in_first_order: # 2. Convert to an ODE derivative for 1st order derivative = (sample - pred_original_sample) / sigma_hat # 3. delta timestep dt = sigma_next - sigma_hat # store for 2nd order step self.prev_derivative = derivative self.dt = dt self.sample = sample else: # 2. 2nd order / Heun's method derivative = (sample - pred_original_sample) / sigma_next derivative = (self.prev_derivative + derivative) / 2 # 3. take prev timestep & sample dt = self.dt sample = self.sample
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# free dt and derivative # Note, this puts the scheduler in "first order mode" self.prev_derivative = None self.dt = None self.sample = None prev_sample = sample + derivative * dt # upon completion increase step index by one self._step_index += 1 if not return_dict: return ( prev_sample, pred_original_sample, ) return HeunDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_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 KDPM2DiscreteSchedulerOutput(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 KDPM2DiscreteScheduler(SchedulerMixin, ConfigMixin): """ KDPM2DiscreteScheduler is inspired by the DPMSolver2 and Algorithm 2 from the [Elucidating the Design Space of Diffusion-Based Generative Models](https://huggingface.co/papers/2206.00364) paper. 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 0.00085): The starting `beta` value of inference. beta_end (`float`, defaults to 0.012): 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`. 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}.
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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. 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). timestep_spacing (`str`, defaults to `"linspace"`): The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
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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, use_karras_sigmas: Optional[bool] = False, use_exponential_sigmas: Optional[bool] = False, use_beta_sigmas: Optional[bool] = False, prediction_type: str = "epsilon", 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( "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used."
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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) # set all values self.set_timesteps(num_train_timesteps, None, num_train_timesteps) 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 if self.config.timestep_spacing in ["linspace", "trailing"]: return self.sigmas.max() return (self.sigmas.max() ** 2 + 1) ** 0.5 @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
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# 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 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. Args: sample (`torch.Tensor`): The input sample. timestep (`int`, *optional*): The current timestep in the diffusion chain.
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Returns: `torch.Tensor`: A scaled input sample. """ if self.step_index is None: self._init_step_index(timestep) if self.state_in_first_order: sigma = self.sigmas[self.step_index] else: sigma = self.sigmas_interpol[self.step_index] sample = sample / ((sigma**2 + 1) ** 0.5) return sample def set_timesteps( self, num_inference_steps: int, device: Union[str, torch.device] = None, num_train_timesteps: Optional[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. """ self.num_inference_steps = num_inference_steps num_train_timesteps = num_train_timesteps or self.config.num_train_timesteps
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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, num_train_timesteps - 1, num_inference_steps, dtype=np.float32)[::-1].copy() elif self.config.timestep_spacing == "leading": step_ratio = 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.float32) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = 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
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timesteps = (np.arange(num_train_timesteps, 0, -step_ratio)).round().copy().astype(np.float32) 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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sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) log_sigmas = np.log(sigmas) sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas) if self.config.use_karras_sigmas: 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 = 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 = 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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self.log_sigmas = torch.from_numpy(log_sigmas).to(device=device) sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32) sigmas = torch.from_numpy(sigmas).to(device=device) # interpolate sigmas sigmas_interpol = sigmas.log().lerp(sigmas.roll(1).log(), 0.5).exp() self.sigmas = torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2), sigmas[-1:]]) self.sigmas_interpol = torch.cat( [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2), sigmas_interpol[-1:]] ) timesteps = torch.from_numpy(timesteps).to(device)
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# interpolate timesteps sigmas_interpol = sigmas_interpol.cpu() log_sigmas = self.log_sigmas.cpu() timesteps_interpol = np.array( [self._sigma_to_t(sigma_interpol, log_sigmas) for sigma_interpol in sigmas_interpol] ) timesteps_interpol = torch.from_numpy(timesteps_interpol).to(device, dtype=timesteps.dtype) interleaved_timesteps = torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None]), dim=-1).flatten() self.timesteps = torch.cat([timesteps[:1], interleaved_timesteps]) self.sample = None self._step_index = None self._begin_index = None self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication @property def state_in_first_order(self): return self.sample is None
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# 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 # 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]
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# 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 # 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 if hasattr(self.config, "sigma_max"): sigma_max = self.config.sigma_max else: sigma_max = None
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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.""" # 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() sigmas = np.exp(np.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps)) return sigmas # 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)"""
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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.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
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def step( self, model_output: Union[torch.Tensor, np.ndarray], timestep: Union[float, torch.Tensor], sample: Union[torch.Tensor, np.ndarray], return_dict: bool = True, ) -> Union[KDPM2DiscreteSchedulerOutput, 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). 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. return_dict (`bool`): Whether or not to return a [`~schedulers.scheduling_k_dpm_2_discrete.KDPM2DiscreteSchedulerOutput`] or tuple.
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Returns: [`~schedulers.scheduling_k_dpm_2_discrete.KDPM2DiscreteSchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_k_dpm_2_discrete.KDPM2DiscreteSchedulerOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor. """ if self.step_index is None: self._init_step_index(timestep) if self.state_in_first_order: sigma = self.sigmas[self.step_index] sigma_interpol = self.sigmas_interpol[self.step_index + 1] sigma_next = self.sigmas[self.step_index + 1] else: # 2nd order / KDPM2's method sigma = self.sigmas[self.step_index - 1] sigma_interpol = self.sigmas_interpol[self.step_index] sigma_next = self.sigmas[self.step_index]
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# currently only gamma=0 is supported. This usually works best anyways. # We can support gamma in the future but then need to scale the timestep before # passing it to the model which requires a change in API gamma = 0 sigma_hat = sigma * (gamma + 1) # Note: sigma_hat == sigma for now
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# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise if self.config.prediction_type == "epsilon": sigma_input = sigma_hat if self.state_in_first_order else sigma_interpol pred_original_sample = sample - sigma_input * model_output elif self.config.prediction_type == "v_prediction": sigma_input = sigma_hat if self.state_in_first_order else sigma_interpol pred_original_sample = model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + ( sample / (sigma_input**2 + 1) ) elif self.config.prediction_type == "sample": raise NotImplementedError("prediction_type not implemented yet: sample") else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`" )
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if self.state_in_first_order: # 2. Convert to an ODE derivative for 1st order derivative = (sample - pred_original_sample) / sigma_hat # 3. delta timestep dt = sigma_interpol - sigma_hat # store for 2nd order step self.sample = sample else: # DPM-Solver-2 # 2. Convert to an ODE derivative for 2nd order derivative = (sample - pred_original_sample) / sigma_interpol # 3. delta timestep dt = sigma_next - sigma_hat sample = self.sample self.sample = None # upon completion increase step index by one self._step_index += 1 prev_sample = sample + derivative * dt if not return_dict: return ( prev_sample, pred_original_sample, ) return KDPM2DiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_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 PNDMSchedulerState: common: CommonSchedulerState final_alpha_cumprod: jnp.ndarray # setable values init_noise_sigma: jnp.ndarray timesteps: jnp.ndarray num_inference_steps: Optional[int] = None prk_timesteps: Optional[jnp.ndarray] = None plms_timesteps: Optional[jnp.ndarray] = None # running values cur_model_output: Optional[jnp.ndarray] = None counter: Optional[jnp.int32] = None cur_sample: Optional[jnp.ndarray] = None ets: Optional[jnp.ndarray] = 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 FlaxPNDMSchedulerOutput(FlaxSchedulerOutput): state: PNDMSchedulerState
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class FlaxPNDMScheduler(FlaxSchedulerMixin, ConfigMixin): """ Pseudo numerical methods for diffusion models (PNDM) proposes using more advanced ODE integration techniques, namely Runge-Kutta method and a linear multi-step method. [`~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/2202.09778
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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. skip_prk_steps (`bool`): allows the scheduler to skip the Runge-Kutta steps that are defined in the original paper as being required before plms steps; defaults to `False`. set_alpha_to_one (`bool`, default `False`): each diffusion step uses the value of alphas product at that step and at the previous one. For the final
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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`, optional): prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4 https://imagen.research.google/video/paper.pdf) 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 pndm_order: int @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, skip_prk_steps: bool = False, set_alpha_to_one: bool = False, steps_offset: int = 0, prediction_type: str = "epsilon", dtype: jnp.dtype = jnp.float32, ): self.dtype = dtype # For now we only support F-PNDM, i.e. the runge-kutta method # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf # mainly at formula (9), (12), (13) and the Algorithm 2. self.pndm_order = 4
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def create_state(self, common: Optional[CommonSchedulerState] = None) -> PNDMSchedulerState: if common is None: common = CommonSchedulerState.create(self) # 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]
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return PNDMSchedulerState.create( common=common, final_alpha_cumprod=final_alpha_cumprod, init_noise_sigma=init_noise_sigma, timesteps=timesteps, ) def set_timesteps(self, state: PNDMSchedulerState, num_inference_steps: int, shape: Tuple) -> PNDMSchedulerState: """ Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference. Args: state (`PNDMSchedulerState`): the `FlaxPNDMScheduler` 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. """
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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() + self.config.steps_offset if self.config.skip_prk_steps: # for some models like stable diffusion the prk steps can/should be skipped to # produce better results. When using PNDM with `self.config.skip_prk_steps` the implementation # is based on crowsonkb's PLMS sampler implementation: https://github.com/CompVis/latent-diffusion/pull/51 prk_timesteps = jnp.array([], dtype=jnp.int32) plms_timesteps = jnp.concatenate([_timesteps[:-1], _timesteps[-2:-1], _timesteps[-1:]])[::-1]
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else: prk_timesteps = _timesteps[-self.pndm_order :].repeat(2) + jnp.tile( jnp.array([0, self.config.num_train_timesteps // num_inference_steps // 2], dtype=jnp.int32), self.pndm_order, ) prk_timesteps = (prk_timesteps[:-1].repeat(2)[1:-1])[::-1] plms_timesteps = _timesteps[:-3][::-1] timesteps = jnp.concatenate([prk_timesteps, plms_timesteps]) # initial running values cur_model_output = jnp.zeros(shape, dtype=self.dtype) counter = jnp.int32(0) cur_sample = jnp.zeros(shape, dtype=self.dtype) ets = jnp.zeros((4,) + shape, dtype=self.dtype)
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return state.replace( timesteps=timesteps, num_inference_steps=num_inference_steps, prk_timesteps=prk_timesteps, plms_timesteps=plms_timesteps, cur_model_output=cur_model_output, counter=counter, cur_sample=cur_sample, ets=ets, ) def scale_model_input( self, state: PNDMSchedulerState, sample: jnp.ndarray, timestep: Optional[int] = None ) -> jnp.ndarray: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. 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
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def step( self, state: PNDMSchedulerState, model_output: jnp.ndarray, timestep: int, sample: jnp.ndarray, return_dict: bool = True, ) -> Union[FlaxPNDMSchedulerOutput, 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). This function calls `step_prk()` or `step_plms()` depending on the internal variable `counter`.
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Args: state (`PNDMSchedulerState`): the `FlaxPNDMScheduler` 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 FlaxPNDMSchedulerOutput class Returns: [`FlaxPNDMSchedulerOutput`] or `tuple`: [`FlaxPNDMSchedulerOutput`] 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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if self.config.skip_prk_steps: prev_sample, state = self.step_plms(state, model_output, timestep, sample) else: prk_prev_sample, prk_state = self.step_prk(state, model_output, timestep, sample) plms_prev_sample, plms_state = self.step_plms(state, model_output, timestep, sample) cond = state.counter < len(state.prk_timesteps) prev_sample = jax.lax.select(cond, prk_prev_sample, plms_prev_sample) state = state.replace( cur_model_output=jax.lax.select(cond, prk_state.cur_model_output, plms_state.cur_model_output), ets=jax.lax.select(cond, prk_state.ets, plms_state.ets), cur_sample=jax.lax.select(cond, prk_state.cur_sample, plms_state.cur_sample), counter=jax.lax.select(cond, prk_state.counter, plms_state.counter), ) if not return_dict: return (prev_sample, state)
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return FlaxPNDMSchedulerOutput(prev_sample=prev_sample, state=state) def step_prk( self, state: PNDMSchedulerState, model_output: jnp.ndarray, timestep: int, sample: jnp.ndarray, ) -> Union[FlaxPNDMSchedulerOutput, Tuple]: """ Step function propagating the sample with the Runge-Kutta method. RK takes 4 forward passes to approximate the solution to the differential equation. Args: state (`PNDMSchedulerState`): the `FlaxPNDMScheduler` 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 FlaxPNDMSchedulerOutput class
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Returns: [`FlaxPNDMSchedulerOutput`] or `tuple`: [`FlaxPNDMSchedulerOutput`] 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" ) diff_to_prev = jnp.where( state.counter % 2, 0, self.config.num_train_timesteps // state.num_inference_steps // 2 ) prev_timestep = timestep - diff_to_prev timestep = state.prk_timesteps[state.counter // 4 * 4] model_output = jax.lax.select( (state.counter % 4) != 3, model_output, # remainder 0, 1, 2 state.cur_model_output + 1 / 6 * model_output, # remainder 3 )
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state = state.replace( cur_model_output=jax.lax.select_n( state.counter % 4, state.cur_model_output + 1 / 6 * model_output, # remainder 0 state.cur_model_output + 1 / 3 * model_output, # remainder 1 state.cur_model_output + 1 / 3 * model_output, # remainder 2 jnp.zeros_like(state.cur_model_output), # remainder 3 ), ets=jax.lax.select( (state.counter % 4) == 0, state.ets.at[0:3].set(state.ets[1:4]).at[3].set(model_output), # remainder 0 state.ets, # remainder 1, 2, 3 ), cur_sample=jax.lax.select( (state.counter % 4) == 0, sample, # remainder 0 state.cur_sample, # remainder 1, 2, 3 ), )
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cur_sample = state.cur_sample prev_sample = self._get_prev_sample(state, cur_sample, timestep, prev_timestep, model_output) state = state.replace(counter=state.counter + 1) return (prev_sample, state) def step_plms( self, state: PNDMSchedulerState, model_output: jnp.ndarray, timestep: int, sample: jnp.ndarray, ) -> Union[FlaxPNDMSchedulerOutput, Tuple]: """ Step function propagating the sample with the linear multi-step method. This has one forward pass with multiple times to approximate the solution.
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Args: state (`PNDMSchedulerState`): the `FlaxPNDMScheduler` 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 FlaxPNDMSchedulerOutput class Returns: [`FlaxPNDMSchedulerOutput`] or `tuple`: [`FlaxPNDMSchedulerOutput`] 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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# NOTE: There is no way to check in the jitted runtime if the prk mode was ran before prev_timestep = timestep - self.config.num_train_timesteps // state.num_inference_steps prev_timestep = jnp.where(prev_timestep > 0, prev_timestep, 0) # Reference: # if state.counter != 1: # state.ets.append(model_output) # else: # prev_timestep = timestep # timestep = timestep + self.config.num_train_timesteps // state.num_inference_steps prev_timestep = jnp.where(state.counter == 1, timestep, prev_timestep) timestep = jnp.where( state.counter == 1, timestep + self.config.num_train_timesteps // state.num_inference_steps, timestep )
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# Reference: # if len(state.ets) == 1 and state.counter == 0: # model_output = model_output # state.cur_sample = sample # elif len(state.ets) == 1 and state.counter == 1: # model_output = (model_output + state.ets[-1]) / 2 # sample = state.cur_sample # state.cur_sample = None # elif len(state.ets) == 2: # model_output = (3 * state.ets[-1] - state.ets[-2]) / 2 # elif len(state.ets) == 3: # model_output = (23 * state.ets[-1] - 16 * state.ets[-2] + 5 * state.ets[-3]) / 12 # else: # model_output = (1 / 24) * (55 * state.ets[-1] - 59 * state.ets[-2] + 37 * state.ets[-3] - 9 * state.ets[-4])
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state = state.replace( ets=jax.lax.select( state.counter != 1, state.ets.at[0:3].set(state.ets[1:4]).at[3].set(model_output), # counter != 1 state.ets, # counter 1 ), cur_sample=jax.lax.select( state.counter != 1, sample, # counter != 1 state.cur_sample, # counter 1 ), ) state = state.replace( cur_model_output=jax.lax.select_n( jnp.clip(state.counter, 0, 4), model_output, # counter 0 (model_output + state.ets[-1]) / 2, # counter 1 (3 * state.ets[-1] - state.ets[-2]) / 2, # counter 2 (23 * state.ets[-1] - 16 * state.ets[-2] + 5 * state.ets[-3]) / 12, # counter 3 (1 / 24) * (55 * state.ets[-1] - 59 * state.ets[-2] + 37 * state.ets[-3] - 9 * state.ets[-4]), # counter >= 4 ), )
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sample = state.cur_sample model_output = state.cur_model_output prev_sample = self._get_prev_sample(state, sample, timestep, prev_timestep, model_output) state = state.replace(counter=state.counter + 1) return (prev_sample, state) def _get_prev_sample(self, state: PNDMSchedulerState, sample, timestep, prev_timestep, model_output): # See formula (9) of PNDM paper https://arxiv.org/pdf/2202.09778.pdf # this function computes x_(t−δ) using the formula of (9) # Note that x_t needs to be added to both sides of the equation
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# Notation (<variable name> -> <name in paper> # alpha_prod_t -> α_t # alpha_prod_t_prev -> α_(t−δ) # beta_prod_t -> (1 - α_t) # beta_prod_t_prev -> (1 - α_(t−δ)) # sample -> x_t # model_output -> e_θ(x_t, t) # prev_sample -> x_(t−δ) 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 if self.config.prediction_type == "v_prediction": model_output = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample elif self.config.prediction_type != "epsilon": raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `v_prediction`" )
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# corresponds to (α_(t−δ) - α_t) divided by # denominator of x_t in formula (9) and plus 1 # Note: (α_(t−δ) - α_t) / (sqrt(α_t) * (sqrt(α_(t−δ)) + sqr(α_t))) = # sqrt(α_(t−δ)) / sqrt(α_t)) sample_coeff = (alpha_prod_t_prev / alpha_prod_t) ** (0.5) # corresponds to denominator of e_θ(x_t, t) in formula (9) model_output_denom_coeff = alpha_prod_t * beta_prod_t_prev ** (0.5) + ( alpha_prod_t * beta_prod_t * alpha_prod_t_prev ) ** (0.5) # full formula (9) prev_sample = ( sample_coeff * sample - (alpha_prod_t_prev - alpha_prod_t) * model_output / model_output_denom_coeff ) return prev_sample def add_noise( self, state: PNDMSchedulerState, original_samples: jnp.ndarray, noise: jnp.ndarray, timesteps: jnp.ndarray, ) -> jnp.ndarray: return add_noise_common(state.common, original_samples, noise, timesteps)
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def __len__(self): return self.config.num_train_timesteps
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class DDIMSchedulerOutput(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 CogVideoXDPMScheduler(SchedulerMixin, ConfigMixin): """ `DDIMScheduler` extends the denoising procedure introduced in denoising diffusion probabilistic models (DDPMs) with non-Markovian guidance. 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`. 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`):
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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), `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.
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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. 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
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[`--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 = 0.00085, beta_end: float = 0.0120, beta_schedule: str = "scaled_linear", trained_betas: Optional[Union[np.ndarray, List[float]]] = None, clip_sample: bool = True, set_alpha_to_one: bool = True, steps_offset: int = 0, prediction_type: str = "epsilon", clip_sample_range: float = 1.0, sample_max_value: float = 1.0, timestep_spacing: str = "leading", rescale_betas_zero_snr: bool = False, snr_shift_scale: float = 3.0, ): 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.float64) ** 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) # Modify: SNR shift following SD3 self.alphas_cumprod = self.alphas_cumprod / (snr_shift_scale + (1 - snr_shift_scale) * self.alphas_cumprod) # Rescale for zero SNR if rescale_betas_zero_snr: self.alphas_cumprod = rescale_zero_terminal_snr(self.alphas_cumprod) # 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
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# setable values self.num_inference_steps = None self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy().astype(np.int64)) def _get_variance(self, timestep, prev_timestep): 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 variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev) return variance 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: int, device: Union[str, torch.device] = None): """ Sets the discrete timesteps used for the diffusion chain (to be run before inference). Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. """
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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
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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": step_ratio = self.config.num_train_timesteps / self.num_inference_steps
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# 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 'leading' or 'trailing'." )
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self.timesteps = torch.from_numpy(timesteps).to(device) def get_variables(self, alpha_prod_t, alpha_prod_t_prev, alpha_prod_t_back=None): lamb = ((alpha_prod_t / (1 - alpha_prod_t)) ** 0.5).log() lamb_next = ((alpha_prod_t_prev / (1 - alpha_prod_t_prev)) ** 0.5).log() h = lamb_next - lamb if alpha_prod_t_back is not None: lamb_previous = ((alpha_prod_t_back / (1 - alpha_prod_t_back)) ** 0.5).log() h_last = lamb - lamb_previous r = h_last / h return h, r, lamb, lamb_next else: return h, None, lamb, lamb_next def get_mult(self, h, r, alpha_prod_t, alpha_prod_t_prev, alpha_prod_t_back): mult1 = ((1 - alpha_prod_t_prev) / (1 - alpha_prod_t)) ** 0.5 * (-h).exp() mult2 = (-2 * h).expm1() * alpha_prod_t_prev**0.5
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if alpha_prod_t_back is not None: mult3 = 1 + 1 / (2 * r) mult4 = 1 / (2 * r) return mult1, mult2, mult3, mult4 else: return mult1, mult2 def step( self, model_output: torch.Tensor, old_pred_original_sample: torch.Tensor, timestep: int, timestep_back: int, sample: torch.Tensor, eta: float = 0.0, use_clipped_model_output: bool = False, generator=None, variance_noise: Optional[torch.Tensor] = None, return_dict: bool = False, ) -> Union[DDIMSchedulerOutput, 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. eta (`float`): The weight of noise for added noise in diffusion step. use_clipped_model_output (`bool`, defaults to `False`): If `True`, computes "corrected" `model_output` from the clipped predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when `self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would coincide with the one provided as input and `use_clipped_model_output` has no effect. generator (`torch.Generator`, *optional*): A random number generator.
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variance_noise (`torch.Tensor`): Alternative to generating noise with `generator` by directly providing the noise for the variance itself. Useful for methods such as [`CycleDiffusion`]. return_dict (`bool`, *optional*, defaults to `True`): Whether or not to return a [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] or `tuple`.
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Returns: [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] 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" ) # 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"
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