diff --git a/test/test_distributions.py b/test/test_distributions.py
index e2e785083f1..770459031f9 100644
--- a/test/test_distributions.py
+++ b/test/test_distributions.py
@@ -921,6 +921,55 @@ def test_entropy(self, neg_inf: float, sparse: bool) -> None:
         entropy = -entropy.sum(dim=-1)
         torch.testing.assert_close(dist.entropy(), entropy)
 
+    @pytest.mark.parametrize(
+        "distribution_cls", [MaskedCategorical, MaskedOneHotCategorical]
+    )
+    @pytest.mark.parametrize("padding_value", [-1, 0])
+    @pytest.mark.parametrize("neg_inf", [float("-inf"), -10.0])
+    @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
+    @pytest.mark.parametrize("device", get_default_devices())
+    def test_entropy_sparse_padding(
+        self, distribution_cls, padding_value, neg_inf, dtype, device
+    ):
+        logits = torch.tensor(
+            [[1.0, 2.0, 3.0, 4.0], [0.0, 3.0, 1.0, 2.0]], dtype=dtype, device=device
+        )
+        logits = logits.expand(2, 2, 4).clone().requires_grad_()
+        indices = torch.tensor(
+            [[1, 2, padding_value], [1, 2, 3]], device=device
+        ).expand(2, 2, 3)
+        distribution = distribution_cls(
+            logits=logits, indices=indices, padding_value=padding_value, neg_inf=neg_inf
+        )
+        actual = distribution.entropy()
+        expected = torch.stack(
+            [
+                torch.distributions.Categorical(logits=logits[:, 0, 1:3]).entropy(),
+                torch.distributions.Categorical(logits=logits[:, 1, 1:]).entropy(),
+            ],
+            dim=-1,
+        )
+        torch.testing.assert_close(actual, expected)
+        actual_grad = torch.autograd.grad(actual.sum(), logits, retain_graph=True)[0]
+        expected_grad = torch.autograd.grad(expected.sum(), logits)[0]
+        torch.testing.assert_close(actual_grad, expected_grad)
+
+    @pytest.mark.parametrize(
+        "distribution_cls", [MaskedCategorical, MaskedOneHotCategorical]
+    )
+    @pytest.mark.parametrize("sparse", [False, True])
+    def test_entropy_zero_probability(self, distribution_cls, sparse):
+        probs = torch.tensor([0.0, 0.2, 0.3, 0.5])
+        mask = torch.tensor([True, False, True, True])
+        indices = torch.tensor([0, 2, 3])
+        distribution = distribution_cls(
+            probs=probs,
+            mask=None if sparse else mask,
+            indices=indices if sparse else None,
+        )
+        expected = torch.distributions.Categorical(probs=probs[indices]).entropy()
+        torch.testing.assert_close(distribution.entropy(), expected)
+
     @pytest.mark.parametrize("neg_inf", [-1e20, float("-inf")])
     def test_sample_sparse(self, neg_inf: float) -> None:
         torch.manual_seed(0)
diff --git a/torchrl/modules/distributions/discrete.py b/torchrl/modules/distributions/discrete.py
index a6a9dc56a4b..8ae19c131c2 100644
--- a/torchrl/modules/distributions/discrete.py
+++ b/torchrl/modules/distributions/discrete.py
@@ -312,13 +312,12 @@ def entropy(self):
 
         # Clamp logits to avoid numerical issues
         logits = self.logits
+        mask = ~logits.isfinite()
         if self._mask.dtype is torch.bool:
-            mask = expand_as_right(self._mask, logits)
-            mask = (~mask) | (~logits.isfinite())
-            logits = torch.masked_fill(logits, mask, min_real)
-        else:
-            # logits are already masked
-            pass
+            mask = mask | ~expand_as_right(self._mask, logits)
+        elif self._padding_value is not None:
+            mask = mask | (self._mask == self._padding_value)
+        logits = torch.masked_fill(logits, mask, min_real)
         logits = logits - logits.logsumexp(-1, keepdim=True)
 
         # Get probabilities and mask them