class_docstr: 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
  
  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.
      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`.
      set_alpha_to_one (`bool`, default `True`):
          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. 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.
      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.
      rescale_betas_zero_snr (`bool`, default `False`):
          whether to rescale the betas to have zero terminal SNR (proposed by https://arxiv.org/pdf/2305.08891.pdf).
          This can enable the model to generate very bright and dark samples instead of limiting it to samples with
          medium brightness. Loosely related to
          [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
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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.
      eta (`float`): weight of noise for added noise in diffusion step.
      use_clipped_model_output (`bool`): if `True`, compute "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` will have not effect.
      generator: random number generator.
      variance_noise (`torch.FloatTensor`): instead of generating noise for the variance using `generator`, we
          can directly provide the noise for the variance itself. This is useful for methods such as
          CycleDiffusion. (https://arxiv.org/abs/2210.05559)
      return_dict (`bool`): option for returning tuple rather than DDIMParallelSchedulerOutput class
  
  Returns:
      [`~schedulers.scheduling_utils.DDIMParallelSchedulerOutput`] or `tuple`:
      [`~schedulers.scheduling_utils.DDIMParallelSchedulerOutput`] 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,
      eta: float = 0.0,
      use_clipped_model_output: bool = False,
      generator=None,
      variance_noise: Optional[torch.FloatTensor] = None,
      return_dict: bool = True,
  ) -> Union[DDIMParallelSchedulerOutput, 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.
          eta (`float`): weight of noise for added noise in diffusion step.
          use_clipped_model_output (`bool`): if `True`, compute "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` will have not effect.
          generator: random number generator.
          variance_noise (`torch.FloatTensor`): instead of generating noise for the variance using `generator`, we
              can directly provide the noise for the variance itself. This is useful for methods such as
              CycleDiffusion. (https://arxiv.org/abs/2210.05559)
          return_dict (`bool`): option for returning tuple rather than DDIMParallelSchedulerOutput class
  
      Returns:
          [`~schedulers.scheduling_utils.DDIMParallelSchedulerOutput`] or `tuple`:
          [`~schedulers.scheduling_utils.DDIMParallelSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`.
          When returning a tuple, 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"
  
      # 1. get previous step value (=t-1)
      prev_timestep = (
          timestep
          - self.config.num_train_timesteps // self.num_inference_steps
      )
  
      # 2. compute alphas, betas
      alpha_prod_t = self.alphas_cumprod[timestep]
      alpha_prod_t_prev = (
          self.alphas_cumprod[prev_timestep]
          if prev_timestep >= 0
          else self.final_alpha_cumprod
      )
  
      beta_prod_t = 1 - alpha_prod_t
  
      # 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`"
          )
  
      # 4. 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,
          )
  
      # 5. 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(timestep, prev_timestep)
      std_dev_t = eta * variance ** (0.5)
  
      if use_clipped_model_output:
          # the pred_epsilon is always re-derived from the clipped x_0 in Glide
          pred_epsilon = (
              sample - alpha_prod_t ** (0.5) * pred_original_sample
          ) / beta_prod_t ** (0.5)
  
      # 6. 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
  
      # 7. 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 eta > 0:
          if variance_noise is not None and generator is not None:
              raise ValueError(
                  "Cannot pass both generator and variance_noise. Please make sure that either `generator` or"
                  " `variance_noise` stays `None`."
              )
  
          if variance_noise is None:
              variance_noise = randn_tensor(
                  model_output.shape,
                  generator=generator,
                  device=model_output.device,
                  dtype=model_output.dtype,
              )
          variance = std_dev_t * variance_noise
  
          prev_sample = prev_sample + variance
  
      if not return_dict:
          return (prev_sample,)
  
      return DDIMParallelSchedulerOutput(
          prev_sample=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 7 for calling the DDIMParallelScheduler obj's underlying member method code with example usage: obj.step(model_output, timestep, sample, eta, use_clipped_model_output, generator, variance_noise, return_dict) and returns: DDIMParallelSchedulerOutput, prev_sample