diff --git a/src/torchjd/scalarization/_geometric_mean.py b/src/torchjd/scalarization/_geometric_mean.py
index f54d9fca..5c71f6d5 100644
--- a/src/torchjd/scalarization/_geometric_mean.py
+++ b/src/torchjd/scalarization/_geometric_mean.py
@@ -15,9 +15,9 @@ class GeometricMean(Scalarizer):
     """
 
     def forward(self, values: Tensor, /) -> Tensor:
-        if (values < 1e-12).any():
+        if (values < 0.0).any():
             raise ValueError(
-                "GeometricMean is only defined for strictly positive values. Found a value "
-                "below 1e-12 in the input."
+                "GeometricMean is only defined for strictly positive values."
+                "Found a negative value in the input."
             )
         return torch.exp(torch.log(values).mean())
diff --git a/tests/unit/scalarization/test_geometric_mean.py b/tests/unit/scalarization/test_geometric_mean.py
index 1fb99ab9..a3e89089 100644
--- a/tests/unit/scalarization/test_geometric_mean.py
+++ b/tests/unit/scalarization/test_geometric_mean.py
@@ -36,16 +36,27 @@ def test_permutation_invariant(losses: Tensor) -> None:
 
 
 @mark.parametrize(
-    "invalid",
+    "negative",
     [
-        tensor_([1.0, 0.0]),
         tensor_([1.0, -1.0]),
-        tensor_([1.0, 1e-13]),
+        tensor_([-1e-13, 2.0]),
+        tensor_([-1.0]),
     ],
 )
-def test_raises_on_non_positive_input(invalid: Tensor) -> None:
+def test_raises_on_negative_input(negative: Tensor) -> None:
     with raises(ValueError):
-        GeometricMean()(invalid)
+        GeometricMean()(negative)
+
+
+def test_returns_zero_when_a_value_is_zero() -> None:
+    # log(0) = -inf, so the geometric mean collapses to 0. This matches the LibMTL behavior;
+    # the gradient is nan, which is expected for this method.
+    assert GeometricMean()(tensor_([1.0, 0.0])) == 0.0
+
+
+def test_does_not_raise_on_tiny_positive_input() -> None:
+    # Tiny but strictly positive values are valid and must not be rejected.
+    assert GeometricMean()(tensor_([1.0, 1e-13])).isfinite()
 
 
 def test_representations() -> None: