I was reading A Guide to Convolutional Arithmetic 8 to understand Transpose Convolution.
From section 4.1

Using this representation, the backward pass is easily obtained by transposing C; in other words, the error is backpropagated by multiplying the loss with C.T. This operation takes a 4-dimensional vector as input and produces a 16-dimensional vector as output, and its connectivity pattern is compatible with C by construction.

When I try this out in pytorch, the error is certainly not equal to multiplying with C.T.
import torch
import torch.nn.functional as F

x = torch.arange(1, 17, dtype=torch.float).resize_(4, 4)
w = torch.rand(3, 3)

Convolve w and x
# Convert x into an "image" tensor with a single channel and part of a mini-batch of size 1
x1 = x.view(1, 1, 4, 4)
x1.requires_grad = True

# Convert w into a conv filter with a single input channel and a single output channel
w1 = w.view(1, 1, 3, 3)
w1.requires_grad = True

y1 = F.conv2d(x1, w1)

Backpropagate
y1.backward(torch.ones_like(y1))
x1.grad

Now create the C matrix as mentioned in the paper.
C = torch.zeros(4, 16, dtype=torch.float)

C[0, :3] = w[0]
C[0, 4:7] = w[1]
C[0, 8:11] = w[2]

C[1, 1:4] = w[0]
C[1, 5:8] = w[1]
C[1, 9:12] = w[2]

C[2, 4:7] = w[0]
C[2, 8:11] = w[1]
C[2, 12:15] = w[2]

C[3, 5:8] = w[0]
C[3, 9:12] = w[1]
C[3, 13:] = w[2]

Multiplying unrolled y1 by C.T will not equal to x1.grad.
torch.mm(C.transpose(0, 1), y1.view(-1, 1)).view(4, 4)

What am I doing wrong?