class_docstr: ## Denoise Diffusion
class_docstr_tok: ["#","#","Denoise","Diffusion"]
docstr: #### Simplified Loss
  
  $$L_{   ext{simple}}(   heta) = \mathbb{E}_{t,x_0, \epsilon} \Bigg[ igg\Vert
  \epsilon -      extcolor{lightgreen}{\epsilon_  heta}(\sqrt{arlpha_t} x_0 + \sqrt{1-arlpha_t}\epsilon, t)
  igg\Vert^2 \Bigg]$$
docstr_tok: ["#","#","#","#","Simplified","Loss","$","$","L_","{","ext","{","simple","}","}","(","heta",")","=","\\mathbb","{","E","}","_","{","t",",","x_0",",","\\epsilon","}","\\Bigg","[","\bigg\\Vert","\\epsilon","-","extcolor","{","lightgreen","}","{","\\epsilon_","heta","}","(","\\sqrt","{","\bar\u0007lpha_t","}","x_0","+","\\sqrt","{","1-\bar\u0007lpha_t","}","\\epsilon",",","t",")","\bigg\\Vert^2","\\Bigg","]","$","$"]
code: def loss(
      self, x0: torch.Tensor, noise: Optional[torch.Tensor] = None
  ):
      """
      #### Simplified Loss
  
      $$L_{\text{simple}}(\theta) = \mathbb{E}_{t,x_0, \epsilon} \Bigg[ \bigg\Vert
      \epsilon - \textcolor{lightgreen}{\epsilon_\theta}(\sqrt{\bar\alpha_t} x_0 + \sqrt{1-\bar\alpha_t}\epsilon, t)
      \bigg\Vert^2 \Bigg]$$
      """
      # Get batch size
      batch_size = x0.shape[0]
      # Get random $t$ for each sample in the batch
      t = torch.randint(
          0,
          self.n_steps,
          (batch_size,),
          device=x0.device,
          dtype=torch.long,
      )
  
      # $\epsilon \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$
      if noise is None:
          noise = torch.randn_like(x0)
  
      # Sample $x_t$ for $q(x_t|x_0)$
      xt = self.q_sample(x0, t, eps=noise)
      # Get $\textcolor{lightgreen}{\epsilon_\theta}(\sqrt{\bar\alpha_t} x_0 + \sqrt{1-\bar\alpha_t}\epsilon, t)$
      eps_theta = self.eps_model(xt, t)
  
      # MSE loss
      return F.mse_loss(noise, eps_theta)
  
file_path: annotated_deep_learning_paper_implementations/labml_nn/diffusion/ddpm/__init__.py
imports: from typing import Tuple, Optional
  import torch
  import torch.nn.functional
  import torch.utils.data
  from torch import nn
  from labml_nn.diffusion.ddpm.utils import gather
label_desc: Use image node_id 5 for calling the DenoiseDiffusion obj's underlying member method code with example usage: obj.loss(x0, noise) and returns: F