class_docstr: `DDIMInverseScheduler` is the reverse scheduler of [`DDIMScheduler`].
  
  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.
  
  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`):
          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 0, otherwise
          it uses the alpha value at step `num_train_timesteps - 1`.
      steps_offset (`int`, defaults to 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 `num_train_timesteps - 1` for the previous alpha
          product.
      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 `"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
          [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
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docstr: 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.FloatTensor`):
          The direct output from learned diffusion model.
      timestep (`float`):
          The current discrete timestep in the diffusion chain.
      sample (`torch.FloatTensor`):
          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.
      variance_noise (`torch.FloatTensor`):
          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_inverse.DDIMInverseSchedulerOutput`] or
          `tuple`.
  
  Returns:
      [`~schedulers.scheduling_ddim_inverse.DDIMInverseSchedulerOutput`] or `tuple`:
          If return_dict is `True`, [`~schedulers.scheduling_ddim_inverse.DDIMInverseSchedulerOutput`] is
          returned, otherwise a tuple is returned where 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,
      variance_noise: Optional[torch.FloatTensor] = None,
      return_dict: bool = True,
  ) -> 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).
  
      Args:
          model_output (`torch.FloatTensor`):
              The direct output from learned diffusion model.
          timestep (`float`):
              The current discrete timestep in the diffusion chain.
          sample (`torch.FloatTensor`):
              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.
          variance_noise (`torch.FloatTensor`):
              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_inverse.DDIMInverseSchedulerOutput`] or
              `tuple`.
  
      Returns:
          [`~schedulers.scheduling_ddim_inverse.DDIMInverseSchedulerOutput`] or `tuple`:
              If return_dict is `True`, [`~schedulers.scheduling_ddim_inverse.DDIMInverseSchedulerOutput`] is
              returned, otherwise a tuple is returned where the first element is the sample tensor.
  
      """
      # 1. get previous step value (=t+1)
      prev_timestep = timestep
      timestep = min(
          timestep
          - self.config.num_train_timesteps // self.num_inference_steps,
          self.num_train_timesteps - 1,
      )
  
      # 2. compute alphas, betas
      # change original implementation to exactly match noise levels for analogous forward process
      alpha_prod_t = (
          self.alphas_cumprod[timestep]
          if timestep >= 0
          else self.initial_alpha_cumprod
      )
      alpha_prod_t_prev = self.alphas_cumprod[prev_timestep]
  
      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.clip_sample:
          pred_original_sample = pred_original_sample.clamp(
              -self.config.clip_sample_range,
              self.config.clip_sample_range,
          )
  
      # 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) ** (
          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, pred_original_sample)
      return DDIMSchedulerOutput(
          prev_sample=prev_sample,
          pred_original_sample=pred_original_sample,
      )
  
file_path: llmga/llmga/diffusers/src/diffusers/schedulers/scheduling_ddim_inverse.py
imports: import math
  from dataclasses import dataclass
  from typing import List, Optional, Tuple, Union
  import numpy
  import torch
  from diffusers.configuration_utils import ConfigMixin, register_to_config
  from diffusers.schedulers.scheduling_utils import SchedulerMixin
  from diffusers.utils import BaseOutput, deprecate
label_desc: Use image node_id 4 for calling the DDIMInverseScheduler obj's underlying member method code with example usage: obj.step(model_output, timestep, sample, eta, use_clipped_model_output, variance_noise, return_dict) and returns: DDIMSchedulerOutput, prev_sample,  pred_original_sample