class_docstr: ## Sampler class
class_docstr_tok: ["#","#","Sampler","class"]
docstr: #### Estimate $x_0$
  
  $$x_0 pprox \hat{x}_0 = rac{1}{\sqrt{arlpha}}
   \Big( x_t - \sqrt{1 - arlpha_t}      extcolor{lightgreen}{\epsilon_  heta}(x_t, t) \Big)$$
docstr_tok: ["#","#","#","#","Estimate","$","x_0","$","$","$","x_0","\u0007pprox","\\hat","{","x","}","_0","=","rac","{","1","}","{","\\sqrt","{","\bar\u0007lpha","}","}","\\Big","(","x_t","-","\\sqrt","{","1","-","\bar\u0007lpha_t","}","extcolor","{","lightgreen","}","{","\\epsilon_","heta","}","(","x_t",",","t",")","\\Big",")","$","$"]
code: def p_x0(self, xt: torch.Tensor, t: torch.Tensor, eps: torch.Tensor):
      """
      #### Estimate $x_0$
  
      $$x_0 \approx \hat{x}_0 = \frac{1}{\sqrt{\bar\alpha}}
       \Big( x_t - \sqrt{1 - \bar\alpha_t} \textcolor{lightgreen}{\epsilon_\theta}(x_t, t) \Big)$$
      """
      # [gather](utils.html) $\bar\alpha_t$
      alpha_bar = gather(self.alpha_bar, t)
  
      # $$x_0 \approx \hat{x}_0 = \frac{1}{\sqrt{\bar\alpha}}
      #  \Big( x_t - \sqrt{1 - \bar\alpha_t} \textcolor{lightgreen}{\epsilon_\theta}(x_t, t) \Big)$$
      return (xt - (1 - alpha_bar) ** 0.5 * eps) / (alpha_bar**0.5)
  
file_path: annotated_deep_learning_paper_implementations/labml_nn/diffusion/ddpm/evaluate.py
imports: import numpy
  import torch
  from matplotlib import pyplot
  from torchvision.transforms.functional import to_pil_image, resize
  from labml import experiment, monit
  from labml_nn.diffusion.ddpm import DenoiseDiffusion, gather
  from labml_nn.diffusion.ddpm.experiment import Configs
label_desc: Use image node_id 10 for calling the Sampler obj's underlying member method code with example usage: obj.p_x0(xt, t, eps) and returns: unknown