class_docstr: `LCMScheduler` 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.
  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 `1`,
          otherwise it uses the alpha value at step 0.
      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 step 0 for the previous alpha product like in Stable
          Diffusion.
      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.
      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
          [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
code: def add_noise(
      self,
      original_samples: torch.FloatTensor,
      noise: torch.FloatTensor,
      timesteps: torch.IntTensor,
  ) -> torch.FloatTensor:
      # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
      alphas_cumprod = self.alphas_cumprod.to(
          device=original_samples.device, dtype=original_samples.dtype
      )
      timesteps = timesteps.to(original_samples.device)
  
      sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5
      sqrt_alpha_prod = sqrt_alpha_prod.flatten()
      while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
          sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
  
      sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5
      sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
      while len(sqrt_one_minus_alpha_prod.shape) < len(
          original_samples.shape
      ):
          sqrt_one_minus_alpha_prod = (
              sqrt_one_minus_alpha_prod.unsqueeze(-1)
          )
  
      noisy_samples = (
          sqrt_alpha_prod * original_samples
          + sqrt_one_minus_alpha_prod * noise
      )
      return noisy_samples
  
imports: import math
  from dataclasses import dataclass
  from typing import Any, Dict, List, Optional, Tuple, Union
  import numpy
  import torch
  from transformers import CLIPImageProcessor, CLIPTextModel, CLIPTokenizer
  from diffusers import AutoencoderKL, ConfigMixin, DiffusionPipeline, SchedulerMixin, UNet2DConditionModel, logging
  from diffusers.configuration_utils import register_to_config
  from diffusers.image_processor import VaeImageProcessor
  from diffusers.pipelines.stable_diffusion import StableDiffusionPipelineOutput
  from diffusers.pipelines.stable_diffusion.safety_checker import StableDiffusionSafetyChecker
  from diffusers.utils import BaseOutput
label_desc: Use image node_id 8 for calling the LCMScheduler obj's underlying member method code with example usage: obj.add_noise(original_samples, noise, timesteps) and returns: noisy_samples