diff --git a/pytensor/link/jax/dispatch/random.py b/pytensor/link/jax/dispatch/random.py
index 678b2dc486..37f9362ed1 100644
--- a/pytensor/link/jax/dispatch/random.py
+++ b/pytensor/link/jax/dispatch/random.py
@@ -409,12 +409,14 @@ def sample_fn(rng_key, size, dtype, n, p):
         sampling_rng = jax.random.split(rng_key, binom_p.shape[0])
 
         def _binomial_sample_fn(carry, p_rng):
-            s, rho = carry
+            remaining_n, remaining_p = carry
             p, rng = p_rng
-            samples = jax.random.binomial(rng, s, p / rho)
-            s = s - samples
-            rho = rho - p
-            return ((s, rho), samples)
+            samples = jnp.where(
+                p == 0, 0, jax.random.binomial(rng, remaining_n, p / remaining_p)
+            )
+            remaining_n -= samples
+            remaining_p -= p
+            return ((remaining_n, remaining_p), samples)
 
         (remain, _), samples = jax.lax.scan(
             _binomial_sample_fn,
diff --git a/tests/link/jax/test_random.py b/tests/link/jax/test_random.py
index 183b629f79..04be3c881e 100644
--- a/tests/link/jax/test_random.py
+++ b/tests/link/jax/test_random.py
@@ -733,6 +733,18 @@ def test_multinomial():
         samples.std(axis=0), np.sqrt(n[0, :, None] * p * (1 - p)), rtol=0.1
     )
 
+    # Test with p=0
+    g = pt.random.multinomial(n=5, p=pt.eye(4))
+    g_fn = compile_random_function([], g, mode="JAX")
+    samples = g_fn()
+    np.testing.assert_array_equal(samples, np.eye(4) * 5)
+
+    # Test with n=0
+    g = pt.random.multinomial(n=0, p=np.ones(4) / 4)
+    g_fn = compile_random_function([], g, mode="JAX")
+    samples = g_fn()
+    np.testing.assert_array_equal(samples, np.zeros(4))
+
 
 @pytest.mark.skipif(not numpyro_available, reason="VonMises dispatch requires numpyro")
 def test_vonmises_mu_outside_circle():