class_docstr: Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and
  Langevin dynamics sampling.
  
  [`~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/2006.11239
  
  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`, `squaredcos_cap_v2` or `sigmoid`.
      trained_betas (`np.ndarray`, optional):
          option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
      variance_type (`str`):
          options to clip the variance used when adding noise to the denoised sample. Choose from `fixed_small`,
          `fixed_small_log`, `fixed_large`, `fixed_large_log`, `learned` or `learned_range`.
      clip_sample (`bool`, default `True`):
          option to clip predicted sample for numerical stability.
      clip_sample_range (`float`, default `1.0`):
          the maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
      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)
      thresholding (`bool`, default `False`):
          whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
          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). Valid only when `thresholding=True`.
      sample_max_value (`float`, default `1.0`):
          the threshold value for dynamic thresholding. Valid only when `thresholding=True`.
      timestep_spacing (`str`, default `"leading"`):
          The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
          Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
      steps_offset (`int`, default `0`):
          an offset added to the inference steps. You can use a combination of `offset=1` and
          `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
          stable diffusion.
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docstr: 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).
  
  Args:
      model_output (`torch.FloatTensor`): direct output from learned diffusion model.
      timestep (`int`): current discrete timestep in the diffusion chain.
      sample (`torch.FloatTensor`):
          current instance of sample being created by diffusion process.
      generator: random number generator.
      return_dict (`bool`): option for returning tuple rather than DDPMParallelSchedulerOutput class
  
  Returns:
      [`~schedulers.scheduling_utils.DDPMParallelSchedulerOutput`] or `tuple`:
      [`~schedulers.scheduling_utils.DDPMParallelSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`.
      When returning a tuple, the first element is the sample tensor.
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code: def step(
      self,
      model_output: torch.FloatTensor,
      timestep: int,
      sample: torch.FloatTensor,
      generator=None,
      return_dict: bool = True,
  ) -> Union[DDPMParallelSchedulerOutput, 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).
  
      Args:
          model_output (`torch.FloatTensor`): direct output from learned diffusion model.
          timestep (`int`): current discrete timestep in the diffusion chain.
          sample (`torch.FloatTensor`):
              current instance of sample being created by diffusion process.
          generator: random number generator.
          return_dict (`bool`): option for returning tuple rather than DDPMParallelSchedulerOutput class
  
      Returns:
          [`~schedulers.scheduling_utils.DDPMParallelSchedulerOutput`] or `tuple`:
          [`~schedulers.scheduling_utils.DDPMParallelSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`.
          When returning a tuple, the first element is the sample tensor.
  
      """
      t = timestep
  
      prev_t = self.previous_timestep(t)
  
      if model_output.shape[1] == sample.shape[
          1
      ] * 2 and self.variance_type in ["learned", "learned_range"]:
          model_output, predicted_variance = torch.split(
              model_output, sample.shape[1], dim=1
          )
      else:
          predicted_variance = None
  
      # 1. compute alphas, betas
      alpha_prod_t = self.alphas_cumprod[t]
      alpha_prod_t_prev = (
          self.alphas_cumprod[prev_t] if prev_t >= 0 else self.one
      )
      beta_prod_t = 1 - alpha_prod_t
      beta_prod_t_prev = 1 - alpha_prod_t_prev
      current_alpha_t = alpha_prod_t / alpha_prod_t_prev
      current_beta_t = 1 - current_alpha_t
  
      # 2. compute predicted original sample from predicted noise also called
      # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
      if self.config.prediction_type == "epsilon":
          pred_original_sample = (
              sample - beta_prod_t ** (0.5) * model_output
          ) / alpha_prod_t ** (0.5)
      elif self.config.prediction_type == "sample":
          pred_original_sample = model_output
      elif self.config.prediction_type == "v_prediction":
          pred_original_sample = (alpha_prod_t**0.5) * sample - (
              beta_prod_t**0.5
          ) * model_output
      else:
          raise ValueError(
              f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or"
              " `v_prediction`  for the DDPMScheduler."
          )
  
      # 3. Clip or threshold "predicted x_0"
      if self.config.thresholding:
          pred_original_sample = self._threshold_sample(
              pred_original_sample
          )
      elif self.config.clip_sample:
          pred_original_sample = pred_original_sample.clamp(
              -self.config.clip_sample_range,
              self.config.clip_sample_range,
          )
  
      # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
      # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
      pred_original_sample_coeff = (
          alpha_prod_t_prev ** (0.5) * current_beta_t
      ) / beta_prod_t
      current_sample_coeff = (
          current_alpha_t ** (0.5) * beta_prod_t_prev / beta_prod_t
      )
  
      # 5. Compute predicted previous sample µ_t
      # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
      pred_prev_sample = (
          pred_original_sample_coeff * pred_original_sample
          + current_sample_coeff * sample
      )
  
      # 6. Add noise
      variance = 0
      if t > 0:
          device = model_output.device
          variance_noise = randn_tensor(
              model_output.shape,
              generator=generator,
              device=device,
              dtype=model_output.dtype,
          )
          if self.variance_type == "fixed_small_log":
              variance = (
                  self._get_variance(
                      t, predicted_variance=predicted_variance
                  )
                  * variance_noise
              )
          elif self.variance_type == "learned_range":
              variance = self._get_variance(
                  t, predicted_variance=predicted_variance
              )
              variance = torch.exp(0.5 * variance) * variance_noise
          else:
              variance = (
                  self._get_variance(
                      t, predicted_variance=predicted_variance
                  )
                  ** 0.5
              ) * variance_noise
  
      pred_prev_sample = pred_prev_sample + variance
  
      if not return_dict:
          return (pred_prev_sample,)
  
      return DDPMParallelSchedulerOutput(
          prev_sample=pred_prev_sample,
          pred_original_sample=pred_original_sample,
      )
  
imports: import math
  from dataclasses import dataclass
  from typing import List, Optional, Tuple, Union
  import numpy
  import torch
  from ..configuration_utils import ConfigMixin, register_to_config
  from ..utils import BaseOutput
  from ..utils.torch_utils import randn_tensor
  from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
label_desc: Use image node_id 6 for calling the DDPMParallelScheduler obj's underlying member method code with example usage: obj.step(model_output, timestep, sample, generator, return_dict) and returns: DDPMParallelSchedulerOutput, pred_prev_sample