A simple way of computing a causal conv1d using a pad+shift on the whole sequence. Implemented as a PyTorch module. (Currently untested with no CUDA support.)

causal_conv1d.py

import torch
import torch.nn as nn
from torch.autograd import Variable

__CUDA__ = torch.cuda.is_available()

class CausalConv1d(nn.Module):
    """
    A causal 1D convolution.
    """
    def __init__(self, kernel_size, in_channels, out_channels, dilation):
        super(CausalConv1d, self).__init__(self)
        
        # attributes:
        self.kernel_size = kernel_size
        self.in_channels = in_channels
        self.dilation = dilation
        
        # modules:
        self.conv1d = torch.nn.Conv1d(in_channels, out_channels,
                                      kernel_size, stride=1,
                                      padding=(kernel_size-1),
                                      dilation=dilation)

    def forward(self, seq):
        """
        Note that Conv1d expects (batch, in_channels, in_length).
        We assume that seq ~ (len(seq), batch, in_channels), so we'll reshape it first.
        """
        seq_ = seq.permute(1,2,0)
        conv1d_out = self.conv1d(seq_).permute(2,0,1)
        # remove k-1 values from the end:
        return conv1d_out[0:-(self.kernel_size-1)]

I think you forgot to pad using
padding = (kernel_size-1) * dilation