I have tensors X of shape `BxNxD`

and Y of shape `BxNxD`

.

I want to compute the pairwise distances for each element in the batch, i.e. I a `BxMxN`

tensor.

How do I do this?

There is some discussion on this topic here: https://github.com/pytorch/pytorch/issues/9406, but I don’t understand it as there are many implementation details while no actual solution is highlighted.

A naive approach would be to use the answer for non-batched pairwise distances as discussed here: Efficient Distance Matrix Computation, i.e.

```
import torch
import numpy as np
B = 32
N = 128
M = 256
D = 3
X = torch.from_numpy(np.random.normal(size=(B, N, D)))
Y = torch.from_numpy(np.random.normal(size=(B, M, D)))
def pairwise_distances(x, y=None):
x_norm = (x**2).sum(1).view(-1, 1)
if y is not None:
y_t = torch.transpose(y, 0, 1)
y_norm = (y**2).sum(1).view(1, -1)
else:
y_t = torch.transpose(x, 0, 1)
y_norm = x_norm.view(1, -1)
dist = x_norm + y_norm - 2.0 * torch.mm(x, y_t)
return torch.clamp(dist, 0.0, np.inf)
out = []
for b in range(B):
out.append(pairwise_distances(X[b], Y[b]))
print(torch.stack(out).shape)
```

How can I do this without looping over B?

Thanks