code: def f_and_g_prod_corrected_diagonal(
      self, t, y_aug, v
  ):  # For Ito diagonal.
      y, adj_y, _, requires_grad = self.get_state(t, y_aug)
      with torch.enable_grad():
          f, g = self.forward_sde.f_and_g(-t, y)
          g_prod = self.forward_sde.prod(g, v)
  
          f_out = self._f_corrected_diagonal(
              f, g, y, adj_y, requires_grad
          )
          g_prod_out = self._g_prod(g_prod, y, adj_y, requires_grad)
          return f_out, g_prod_out
  
imports: import torch
  from .None import base_sde
  from .None import misc
  from ..settings import NOISE_TYPES, SDE_TYPES
  from ..types import Sequence, TensorOrTensors
label_desc: Use image node_id 16 for calling the AdjointSDE obj's underlying member method code with example usage: obj.f_and_g_prod_corrected_diagonal(t, y_aug, v) and returns: f_out,  g_prod_out