code: def euler_method(
      self,
      x,
      i,
      encoder_hidden_states=None,
      guidance_scale=None,
      s_churn=80,
      s_tmin=0.05,
      s_tmax=50,
      s_noise=1.003,
  ):
      # euler method, omitting second order correction @ lines 9-11 (algorithm 2)
      t, t_next = self.heun_sigmas[i], self.heun_sigmas[i + 1]
  
      eps = torch.randn_like(x) * s_noise
      gamma = (
          min(s_churn / self.num_sample_steps, msqrt(2) - 1)
          if s_tmin <= t <= s_tmax
          else 0
      )
      t_hat = t + gamma * t
      if self.ddpm:
          t_hat = self.ddpm_sigmas[
              torch.abs(self.ddpm_sigmas - t_hat).argmin()
          ]  # iddpm practical, step 3
      x_hat = (
          x + msqrt(max(t_hat**2 - t**2, 0)) * eps
      )  # gamma < 0 -> negative sqrt
      d = (
          x_hat
          - self.d_theta(
              x_hat, t_hat, encoder_hidden_states, guidance_scale
          )
      ) / t_hat
      x_next = x_hat + (t_next - t_hat) * d
  
      return x_next, x_hat, t_next, t_hat, d
  
file_path: diffusion-for-beginners/samplers/heun.py
imports: import torch
  from math import sqrt
label_desc: Use image node_id 10 for calling the HeunSampler obj's underlying member method code with example usage: obj.euler_method(x, i, encoder_hidden_states, guidance_scale, s_churn, s_tmin, s_tmax, s_noise) and returns: x_next,  x_hat,  t_next,  t_hat,  d