EDIT
Hmm, seems they added a lot of padding classes since I looked last time and this is not needed anymore…
This page 2.0k has all the padding you might want 

Padding, whilst copying the values of the tensor is doable with the Functional interface of PyTorch.
You can read more about the different padding modes here 717.
import torch.nn.functional as F

# Pad last 2 dimensions of tensor with (0, 1) -> Adds extra column/row to the right and bottom, whilst copying the values of the current last column/row
padded_tensor = F.pad(input_tensor, (0,1,0,1), mode='replicate')

You can wrap this functional interface in a module:
import torch
import torch.nn.functional as F

class CustomPad(torch.nn.module):
  def __init__(self, padding):
    self.padding = padding
  def forward(self, x):
    return F.pad(x. self.padding, mode='replicate')