class_docstr: Implements DiffGrad algorithm.
  
  It has been proposed in `DiffGrad: An Optimization Method for
  Convolutional Neural Networks`__.
  
  Arguments:
      params: iterable of parameters to optimize or dicts defining
          parameter groups
      lr: learning rate (default: 1e-3)
      betas: coefficients used for computing
          running averages of gradient and its square (default: (0.9, 0.999))
      eps: term added to the denominator to improve
          numerical stability (default: 1e-8)
      weight_decay: weight decay (L2 penalty) (default: 0)
  
  Example:
      >>> import torch_optimizer as optim
      >>> optimizer = optim.DiffGrad(model.parameters(), lr=0.1)
      >>> optimizer.zero_grad()
      >>> loss_fn(model(input), target).backward()
      >>> optimizer.step()
  
  __ https://arxiv.org/abs/1909.11015
  
  Note:
      Reference code: https://github.com/shivram1987/diffGrad
docstr: Performs a single optimization step.
  
  Arguments:
      closure: A closure that reevaluates the model and returns the loss.
docstr_tok: ["Performs","a","single","optimization","step",".","Arguments",":","closure",":","A","closure","that","reevaluates","the","model","and","returns","the","loss","."]
code: def step(self, closure: OptLossClosure = None) -> OptFloat:
      r"""Performs a single optimization step.
  
      Arguments:
          closure: A closure that reevaluates the model and returns the loss.
      """
      loss = None
      if closure is not None:
          loss = closure()
  
      for group in self.param_groups:
          beta1, beta2 = group["betas"]
  
          for p in group["params"]:
              if p.grad is None:
                  continue
              grad = p.grad.data
              if grad.is_sparse:
                  msg = (
                      "DiffGrad does not support sparse gradients, "
                      "please consider SparseAdam instead"
                  )
                  raise RuntimeError(msg)
  
              state = self.state[p]
  
              # State initialization
              if len(state) == 0:
                  state["step"] = 0
                  # Exponential moving average of gradient values
                  state["exp_avg"] = torch.zeros_like(
                      p, memory_format=torch.preserve_format
                  )
                  # Exponential moving average of squared gradient values
                  state["exp_avg_sq"] = torch.zeros_like(
                      p, memory_format=torch.preserve_format
                  )
                  # Previous gradient
                  state["previous_grad"] = torch.zeros_like(
                      p, memory_format=torch.preserve_format
                  )
  
              exp_avg, exp_avg_sq, previous_grad = (
                  state["exp_avg"],
                  state["exp_avg_sq"],
                  state["previous_grad"],
              )
  
              state["step"] += 1
  
              if group["weight_decay"] != 0:
                  grad.add_(p.data, alpha=group["weight_decay"])
  
              # Decay the first and second moment running average coefficient
              exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
              exp_avg_sq.mul_(beta2).addcmul_(
                  grad, grad, value=1 - beta2
              )
              denom = exp_avg_sq.sqrt().add_(group["eps"])
  
              bias_correction1 = 1 - beta1 ** state["step"]
              bias_correction2 = 1 - beta2 ** state["step"]
  
              # compute diffgrad coefficient (dfc)
              diff = torch.abs(previous_grad - grad)
              dfc = torch.div(1.0, (1.0 + torch.exp(-diff)))
              state["previous_grad"] = grad.clone()
  
              # update momentum with dfc
              exp_avg1 = exp_avg * dfc
  
              step_size = (
                  group["lr"]
                  * math.sqrt(bias_correction2)
                  / bias_correction1
              )
  
              p.data.addcdiv_(exp_avg1, denom, value=-step_size)
  
      return loss
  
imports: import math
  import torch
  from torch.optim.optimizer import Optimizer
  from .types import Betas2, OptFloat, OptLossClosure, Params
label_desc: Use image node_id 2 for calling the DiffGrad obj's underlying member method code with example usage: obj.step(closure) and returns: loss