diff --git a/optax/losses/_classification.py b/optax/losses/_classification.py
index 95e09f32a..64d882c54 100644
--- a/optax/losses/_classification.py
+++ b/optax/losses/_classification.py
@@ -815,9 +815,17 @@ def loop_body(prev, x):
   logalpha_phi_last = update_phi_score(logalpha_phi[-1], logalpha_emit[-1])
   logalpha_phi = logalpha_phi.at[-1].set(logalpha_phi_last)
 
+  # Probabilities cannot exceed 1.0 (log-probabilities cannot exceed 0.0). Due
+  # to float32 rounding in log_softmax and logaddexp, values can round slightly
+  # above zero for confident predictions. Clamp to maintain mathematical bounds.
+  logalpha_phi = jnp.minimum(logalpha_phi, 0.0)
+  logalpha_emit = jnp.minimum(logalpha_emit, 0.0)
+  logalpha_phi_last = logalpha_phi[-1]
+
   # extract per_seq_loss
   one_hot = jax.nn.one_hot(labellens, num_classes=maxlabellen + 1)  # [B, N+1]
   per_seq_loss = -jnp.einsum('bn,bn->b', logalpha_phi_last, one_hot)  # pylint:disable=invalid-unary-operand-type
+  per_seq_loss = jnp.maximum(per_seq_loss, 0.0)
 
   return per_seq_loss, logalpha_phi, logalpha_emit
 
diff --git a/optax/losses/_classification_test.py b/optax/losses/_classification_test.py
index da2b8173a..bdc7fda0e 100644
--- a/optax/losses/_classification_test.py
+++ b/optax/losses/_classification_test.py
@@ -963,6 +963,38 @@ def test_repeat_with_one_to_one_alignment(self):
           jnp.array(expected_loss), per_seq_loss[n], rtol=self._rtol
       )
 
+  def test_confident_alignment_nonnegative(self):
+    # Tests that CTC loss and forward log-probabilities do not violate their
+    # theoretical bounds due to float32 rounding for confident alignments.
+    # See https://github.com/google-deepmind/optax/issues/1771
+    logits = jnp.array([[[0.0, 17.0], [0.0, 17.0]]], dtype=jnp.float32)
+    loss, logalpha_phi, logalpha_emit = jax.jit(
+        _classification.ctc_loss_with_forward_probs,
+        static_argnames=('blank_id',),
+    )(
+        logits=logits,
+        logit_paddings=jnp.zeros((1, 2)),
+        labels=jnp.array([[1]], dtype=jnp.int32),
+        label_paddings=jnp.zeros((1, 1)),
+        blank_id=0,
+    )
+    self.assertTrue(jnp.all(loss >= 0.0))
+    self.assertTrue(jnp.all(logalpha_phi <= 0.0))
+    self.assertTrue(jnp.all(logalpha_emit <= 0.0))
+
+    loss_direct = jax.jit(
+        _classification.ctc_loss,
+        static_argnames=('blank_id',),
+    )(
+        logits=logits,
+        logit_paddings=jnp.zeros((1, 2)),
+        labels=jnp.array([[1]], dtype=jnp.int32),
+        label_paddings=jnp.zeros((1, 1)),
+        blank_id=0,
+    )
+    self.assertTrue(jnp.all(loss_direct >= 0.0))
+    np.testing.assert_allclose(loss_direct, 0.0, atol=1e-6)
+
 
 class SigmoidFocalLossTest(parameterized.TestCase):