diff --git a/openwam/model/kernels/attention.py b/openwam/model/kernels/attention.py
index a0f5b378..50b8498d 100644
--- a/openwam/model/kernels/attention.py
+++ b/openwam/model/kernels/attention.py
@@ -10,6 +10,11 @@
 cuDNN attention has no deterministic implementation (PyTorch finds no kernel
 under ``torch.use_deterministic_algorithms(True)``), so in deterministic mode
 ``sdpa`` is the default call. Off by default: PyTorch's backend selection.
+
+When cuDNN is preferred, calls that autograd will differentiate pad K/V to a
+multiple of the cuDNN key tile (see ``_pad_kv_for_cudnn``): the backward kernels
+shipped with PyTorch 2.7 can otherwise return NaN query gradients when the key
+length is not a multiple of 128.
 """
 
 from __future__ import annotations
@@ -71,6 +76,51 @@ def _zero_masked_rows(out: torch.Tensor, nonempty: torch.Tensor) -> torch.Tensor
     return out.permute(order).masked_fill(empty, 0.0).permute(inverse)
 
 
+# The cuDNN SDPA backward bundled with PyTorch 2.7 (cudnn-frontend 1.10, cuDNN 9.7) computes the last key tile
+# without a padding mask when s_kv is not a multiple of 128, so the out-of-range key columns score 0 there. The
+# forward pass is unaffected, but for a query row whose visible logits are all very negative (logsumexp below about
+# -88.7, e.g. keys sharing a large component) the backward evaluates exp(0 - lse) = inf and inf * 0 = NaN in that
+# row of dQ, which then poisons every parameter upstream of Q (NVIDIA/cudnn-frontend#160, pytorch/pytorch#166211;
+# cudnn-frontend >= 1.15 applies a padding mask itself). Padding K/V with zero keys that the mask hides removes the
+# out-of-range columns; the hidden keys get exactly zero attention, so outputs and K/V/Q gradients are unchanged.
+# Only calls that will be differentiated are padded: the forward kernel is not affected.
+_CUDNN_KV_TILE = 128
+
+
+def _pad_seq(x: torch.Tensor, pad: int) -> torch.Tensor:
+    """Append ``pad`` zero rows to the sequence axis (-2) of ``x``, keeping its physical axis order."""
+    # q/k/v are often BSHD buffers viewed as BHSD; keep that layout (cf. ``_zero_masked_rows``). Broadcast
+    # (stride-0) axes go outermost so they do not become the innermost axis of the new buffer.
+    order = sorted(range(x.ndim), key=lambda axis: (x.stride(axis) == 0, x.stride(axis)), reverse=True)
+    inverse = [order.index(axis) for axis in range(x.ndim)]
+    physical = x.permute(order)
+    axis = order.index(x.ndim - 2)
+    shape = list(physical.shape)
+    shape[axis] += pad
+    # Zero-filled buffer + copy_ (vectorized for bf16, unlike torch.cat in PyTorch 2.7); autograd routes the
+    # gradient of the copied slice back to ``x``.
+    padded = physical.new_zeros(shape)
+    padded.narrow(axis, 0, physical.shape[axis]).copy_(physical)
+    return padded.permute(inverse)
+
+
+def _pad_kv_for_cudnn(k: torch.Tensor, v: torch.Tensor, attn_mask):
+    """Pad K/V to a multiple of the cuDNN key tile and hide the padded keys in the (bool or additive) mask."""
+    s_kv = k.shape[-2]
+    pad = -s_kv % _CUDNN_KV_TILE
+    if pad == 0:
+        return k, v, attn_mask
+    k, v = _pad_seq(k, pad), _pad_seq(v, pad)
+    if attn_mask is None:  # key-padding mask that broadcasts against any query shape of the same rank
+        attn_mask = torch.ones(*([1] * (k.ndim - 1)), s_kv + pad, dtype=torch.bool, device=k.device)
+        attn_mask[..., s_kv:] = False
+        return k, v, attn_mask
+    if attn_mask.shape[-1] != s_kv:  # broadcast over keys: materialize the key axis before extending it
+        attn_mask = attn_mask.expand(*attn_mask.shape[:-1], s_kv)
+    hidden = attn_mask.new_full((*attn_mask.shape[:-1], pad), False if attn_mask.dtype == torch.bool else -torch.inf)
+    return k, v, torch.cat([attn_mask, hidden], dim=-1)
+
+
 def sdpa(q: torch.Tensor, k: torch.Tensor, v: torch.Tensor, attn_mask=None) -> torch.Tensor:
     """``F.scaled_dot_product_attention(q, k, v, attn_mask=attn_mask)``, cuDNN first when enabled."""
     if not _PREFER_CUDNN or not q.is_cuda or torch.are_deterministic_algorithms_enabled():
@@ -80,6 +130,8 @@ def sdpa(q: torch.Tensor, k: torch.Tensor, v: torch.Tensor, attn_mask=None) -> t
     nonempty = None
     if attn_mask is not None:
         attn_mask, nonempty = _safe_cudnn_mask(attn_mask)
+    if torch.is_grad_enabled() and (q.requires_grad or k.requires_grad or v.requires_grad):
+        k, v, attn_mask = _pad_kv_for_cudnn(k, v, attn_mask)  # backward-only issue: inference stays unpadded
     with sdpa_kernel(_order(), set_priority=True):
         out = F.scaled_dot_product_attention(q, k, v, attn_mask=attn_mask)
     return out if nonempty is None else _zero_masked_rows(out, nonempty)
diff --git a/tests/test_sdpa_kv_padding.py b/tests/test_sdpa_kv_padding.py
new file mode 100644
index 00000000..679562ed
--- /dev/null
+++ b/tests/test_sdpa_kv_padding.py
@@ -0,0 +1,191 @@
+"""K/V padding that keeps the cuDNN SDPA backward finite when s_kv is not a multiple of the key tile."""
+
+import pytest
+import torch
+import torch.nn.functional as F
+from torch.nn.attention import SDPBackend, sdpa_kernel
+
+from openwam.model.kernels import attention
+
+
+def _mask(kind, sq, skv, *, device="cpu", dtype=torch.float64):
+    if kind is None:
+        return None
+    keep = torch.ones(2, 1, sq, skv, dtype=torch.bool, device=device)
+    keep[:, :, : sq // 3, skv // 2 :] = False
+    if kind == "bool":
+        return keep
+    bias = torch.zeros(keep.shape, dtype=dtype, device=device).masked_fill(~keep, -torch.inf)
+    bias[0, :, :3, :5] = -0.25  # finite biases must survive the padding unchanged
+    return bias
+
+
+def _grads(fn, qkv, mask, upstream):
+    q, k, v = [x.detach().clone().requires_grad_() for x in qkv]
+    out = fn(q, k, v, mask)
+    return out, torch.autograd.grad(out, (q, k, v), upstream)
+
+
+def _math(q, k, v, mask):
+    with sdpa_kernel(SDPBackend.MATH):
+        return F.scaled_dot_product_attention(q, k, v, attn_mask=mask)
+
+
+@pytest.mark.parametrize("transposed", [False, True])
+def test_pad_seq_appends_zero_keys_and_keeps_the_physical_layout(transposed):
+    x = torch.randn(2, 3, 5, 4)
+    if transposed:  # BSHD buffer viewed as BHSD
+        x = x.transpose(1, 2).contiguous().transpose(1, 2)
+    padded = attention._pad_seq(x, 3)
+    assert padded.shape == (2, 3, 8, 4)
+    torch.testing.assert_close(padded[:, :, :5], x, rtol=0, atol=0)
+    assert torch.count_nonzero(padded[:, :, 5:]) == 0
+    order = sorted(range(4), key=x.stride().__getitem__, reverse=True)
+    assert sorted(range(4), key=padded.stride().__getitem__, reverse=True) == order
+
+
+@pytest.mark.parametrize("skv", [128, 256])
+def test_tile_multiples_are_left_untouched(skv):
+    k = torch.randn(1, 2, skv, 8)
+    v = torch.randn(1, 2, skv, 8)
+    mask = torch.ones(1, 1, 3, skv, dtype=torch.bool)
+    pk, pv, pmask = attention._pad_kv_for_cudnn(k, v, mask)
+    assert pk is k and pv is v and pmask is mask
+
+
+@pytest.mark.parametrize("kind", ["bool", "additive", None])
+@pytest.mark.parametrize("skv", [77, 392, 64])
+def test_padding_preserves_outputs_and_gradients_cpu(kind, skv):
+    torch.manual_seed(3)
+    sq = 50
+    qkv = [torch.randn(2, 4, s, 16, dtype=torch.float64) for s in (sq, skv, skv)]
+    mask = _mask(kind, sq, skv)
+    upstream = torch.randn(2, 4, sq, 16, dtype=torch.float64)
+
+    def padded(q, k, v, m):
+        k, v, m = attention._pad_kv_for_cudnn(k, v, m)
+        assert k.shape[-2] % attention._CUDNN_KV_TILE == 0
+        return _math(q, k, v, m)
+
+    ref, ref_grads = _grads(_math, qkv, mask, upstream)
+    out, grads = _grads(padded, qkv, mask, upstream)
+    torch.testing.assert_close(out, ref, rtol=1e-12, atol=1e-12)
+    for got, want in zip(grads, ref_grads):
+        torch.testing.assert_close(got, want, rtol=1e-12, atol=1e-12)
+
+
+def test_three_dimensional_inputs_without_mask_keep_their_rank():
+    torch.manual_seed(5)
+    q, k, v = (torch.randn(3, s, 8, dtype=torch.float64) for s in (6, 77, 77))
+    pk, pv, pmask = attention._pad_kv_for_cudnn(k, v, None)
+    assert pmask.shape == (1, 1, 128)  # same rank as the (B, L, S) logits of a 3-D call
+    assert pmask[..., :77].all() and not pmask[..., 77:].any()
+    out = _math(q, pk, pv, pmask)
+    assert out.shape == (3, 6, 8)
+    torch.testing.assert_close(out, _math(q, k, v, None), rtol=1e-12, atol=1e-12)
+
+
+def test_key_broadcast_mask_is_materialized_before_padding():
+    k, v = torch.randn(1, 2, 5, 4), torch.randn(1, 2, 5, 4)
+    mask = torch.tensor([True, False])[:, None, None, None].expand(2, 1, 3, 1)
+    _, _, pmask = attention._pad_kv_for_cudnn(k, v, mask)
+    assert pmask.shape == (2, 1, 3, 128)
+    assert pmask[0, ..., :5].all() and not pmask[0, ..., 5:].any()
+    assert not pmask[1].any()
+
+
+def _low_lse_inputs(sq, skv, *, device="cuda", dtype=torch.bfloat16, bshd=False, head_dim=128, row=5):
+    """Keys sharing a large component and one query row anti-aligned with it: that row's logits are all about
+    -136, so its logsumexp is far below -88.7 - the condition that turns the out-of-range key columns of the last
+    cuDNN tile into exp(0 - lse) = inf in the backward pass."""
+    torch.manual_seed(0)
+    common = torch.ones(head_dim, device=device, dtype=dtype)
+    q = torch.randn(2, 4, sq, head_dim, device=device, dtype=dtype)
+    q[:, :, row] = -(136.0 / head_dim**0.5) * common
+    k = torch.randn(2, 4, skv, head_dim, device=device, dtype=dtype) * 0.5 + common
+    v = torch.randn(2, 4, skv, head_dim, device=device, dtype=dtype)
+    if bshd:  # the callers pass BSHD buffers viewed as BHSD
+        q, k, v = (x.transpose(1, 2).contiguous().transpose(1, 2) for x in (q, k, v))
+    return q, k, v
+
+
+@pytest.mark.gpu
+@pytest.mark.skipif(not torch.cuda.is_available(), reason="needs CUDA/cuDNN")
+@pytest.mark.parametrize("bshd", [False, True])
+@pytest.mark.parametrize("kind", ["bool", "additive", None])
+@pytest.mark.parametrize("sq,skv", [(392, 392), (360, 64), (100, 77), (256, 392), (128, 64)])
+def test_cudnn_low_logsumexp_rows_have_finite_gradients(monkeypatch, kind, sq, skv, bshd):
+    monkeypatch.setattr(attention, "_PREFER_CUDNN", True)
+    # Force the affected backend; a silent fallback to another kernel cannot pass this test.
+    monkeypatch.setattr(attention, "_order", lambda: [SDPBackend.CUDNN_ATTENTION])
+    qkv = _low_lse_inputs(sq, skv, bshd=bshd)
+    mask = _mask(kind, sq, skv, device="cuda", dtype=torch.bfloat16)
+    upstream = torch.randn(2, 4, sq, 128, device="cuda", dtype=torch.bfloat16)
+
+    def wrapper(q, k, v, m):
+        return attention.sdpa(q, k, v, attn_mask=m)
+
+    def reference(q, k, v, m):
+        m32 = m if m is None or m.dtype == torch.bool else m.float()
+        return _math(q.float(), k.float(), v.float(), m32).to(q.dtype)
+
+    out, grads = _grads(wrapper, qkv, mask, upstream)
+    ref, ref_grads = _grads(reference, qkv, mask, upstream)
+    assert torch.isfinite(out).all()
+    assert all(torch.isfinite(g).all() for g in grads)
+    torch.testing.assert_close(out, ref, rtol=0.02, atol=0.02)
+    for got, want in zip(grads, ref_grads):
+        torch.testing.assert_close(got.float(), want.float(), rtol=0.05, atol=0.05 * want.float().abs().max().item())
+
+
+@pytest.mark.gpu
+@pytest.mark.skipif(not torch.cuda.is_available(), reason="needs CUDA/cuDNN")
+@pytest.mark.parametrize("head_dim", [64, 128])
+@pytest.mark.parametrize("sq,skv", [(392, 392), (100, 77)])
+def test_cudnn_low_logsumexp_row_in_last_query_tile(monkeypatch, head_dim, sq, skv):
+    """Same regression with the low row in the last, partial query tile and 64-wide heads (Cosmos bridges)."""
+    monkeypatch.setattr(attention, "_PREFER_CUDNN", True)
+    monkeypatch.setattr(attention, "_order", lambda: [SDPBackend.CUDNN_ATTENTION])
+    qkv = _low_lse_inputs(sq, skv, head_dim=head_dim, row=sq - 1)
+    mask = _mask("bool", sq, skv, device="cuda")
+    upstream = torch.randn(2, 4, sq, head_dim, device="cuda", dtype=torch.bfloat16)
+
+    def reference(q, k, v, m):
+        return _math(q.float(), k.float(), v.float(), m).to(q.dtype)
+
+    out, grads = _grads(lambda q, k, v, m: attention.sdpa(q, k, v, attn_mask=m), qkv, mask, upstream)
+    ref, ref_grads = _grads(reference, qkv, mask, upstream)
+    assert all(torch.isfinite(g).all() for g in grads)
+    torch.testing.assert_close(out, ref, rtol=0.02, atol=0.02)
+    for got, want in zip(grads, ref_grads):
+        torch.testing.assert_close(got.float(), want.float(), rtol=0.05, atol=0.05 * want.float().abs().max().item())
+
+
+@pytest.mark.gpu
+@pytest.mark.skipif(not torch.cuda.is_available(), reason="needs CUDA/cuDNN")
+@pytest.mark.parametrize(
+    "grad_enabled,requires_grad,padded", [(False, True, False), (True, False, False), (True, True, True)]
+)
+def test_only_differentiated_calls_are_padded(monkeypatch, grad_enabled, requires_grad, padded):
+    """The issue is backward-only: calls autograd will not differentiate keep the original cuDNN forward bit for bit."""
+    monkeypatch.setattr(attention, "_PREFER_CUDNN", True)
+    monkeypatch.setattr(attention, "_order", lambda: [SDPBackend.CUDNN_ATTENTION])
+    calls = []
+    real = attention._pad_kv_for_cudnn
+
+    def spy(*args):
+        calls.append(1)
+        return real(*args)
+
+    monkeypatch.setattr(attention, "_pad_kv_for_cudnn", spy)
+    q, k, v = (x.requires_grad_(requires_grad) for x in _low_lse_inputs(392, 392))
+    mask = _mask("bool", 392, 392, device="cuda")
+    with torch.set_grad_enabled(grad_enabled):
+        out = attention.sdpa(q, k, v, attn_mask=mask)
+    assert bool(calls) == padded
+    with torch.no_grad(), sdpa_kernel(SDPBackend.CUDNN_ATTENTION):
+        reference = F.scaled_dot_product_attention(q, k, v, attn_mask=mask)
+    if padded:
+        torch.testing.assert_close(out, reference, rtol=0.02, atol=0.02)
+    else:
+        torch.testing.assert_close(out, reference, rtol=0, atol=0)