code: def sample_heun(
      denoiser,
      x,
      sigmas,
      generator,
      progress=False,
      callback=None,
      s_churn=0.0,
      s_tmin=0.0,
      s_tmax=float("inf"),
      s_noise=1.0,
  ):
      """Implements Algorithm 2 (Heun steps) from Karras et al. (2022)."""
      s_in = x.new_ones([x.shape[0]])
      indices = range(len(sigmas) - 1)
      if progress:
          from tqdm.auto import tqdm
  
          indices = tqdm(indices)
  
      for i in indices:
          gamma = (
              min(s_churn / (len(sigmas) - 1), 2**0.5 - 1)
              if s_tmin <= sigmas[i] <= s_tmax
              else 0.0
          )
          eps = generator.randn_like(x) * s_noise
          sigma_hat = sigmas[i] * (gamma + 1)
          if gamma > 0:
              x = x + eps * (sigma_hat**2 - sigmas[i] ** 2) ** 0.5
          denoised = denoiser(x, sigma_hat * s_in)
          d = to_d(x, sigma_hat, denoised)
          if callback is not None:
              callback(
                  {
                      "x": x,
                      "i": i,
                      "sigma": sigmas[i],
                      "sigma_hat": sigma_hat,
                      "denoised": denoised,
                  }
              )
          dt = sigmas[i + 1] - sigma_hat
          if sigmas[i + 1] == 0:
              # Euler method
              x = x + d * dt
          else:
              # Heun's method
              x_2 = x + d * dt
              denoised_2 = denoiser(x_2, sigmas[i + 1] * s_in)
              d_2 = to_d(x_2, sigmas[i + 1], denoised_2)
              d_prime = (d + d_2) / 2
              x = x + d_prime * dt
      return x
  
imports: import random
  import numpy
  import torch
  import torch.nn
  import torch.nn.functional
  from piq import LPIPS
  from torchvision.transforms import RandomCrop
  from .None import dist_util
  from .nn import mean_flat, append_dims, append_zero
  from .random_util import get_generator
label_desc: Use image node_id 8 for calling a global function with example usage: sample_heun(denoiser, x, sigmas, generator, progress, callback, s_churn, s_tmin, s_tmax, s_noise) and returns: x