diff --git a/test/test_integrate.py b/test/test_integrate.py
index 555d6ade..db5794c0 100644
--- a/test/test_integrate.py
+++ b/test/test_integrate.py
@@ -792,3 +792,51 @@ def func(self, terms, t0, y0, args):
                 ValueError, match=r"Terms are not compatible with solver!"
             ):
                 diffrax.diffeqsolve(term, solver, 0.0, 1.0, 0.1, y0)
+
+
+def test_vmap_backprop():
+    
+    def dynamics(t, y, args):
+        param = args
+        return param - y
+    
+    
+    def event_fn(t, y, args, **kwargs):
+        return y - 1.5
+    
+    def single_loss_fn(param):
+        solver = diffrax.Euler()
+        root_finder = optx.Newton(1e-2, 1e-2, optx.rms_norm)
+        event = diffrax.Event(event_fn, root_finder)
+        term = diffrax.ODETerm(dynamics)
+    
+        sol = diffrax.diffeqsolve(
+            term,
+            solver=solver,
+            t0=0.0,
+            t1=2.0,
+            dt0=0.1,
+            y0=0.0,
+            args=param,
+            event=event,
+            max_steps=1000,
+        )
+    
+        final_y = sol.ys[-1]
+        return param**2 + final_y**2
+    
+    def batched_loss_fn(params: jnp.ndarray) -> jnp.ndarray:
+        return jax.vmap(single_loss_fn)(params)
+    
+    def grad_fn(params: jnp.ndarray) -> jnp.ndarray:
+        return jax.grad(lambda p: jnp.sum(batched_loss_fn(p)))(params)
+    
+    try:
+        grad = grad_fn(y0)
+    except NotImplementedError as e:
+        pytest.fail(f"NotImplementedError was raised: {e}")
+    except Exception as e:
+        pytest.fail(f"An unexpected exception was raised: {e}")
+
+    assert not jnp.isnan(grad), "Gradient should not be NaN."
+    assert not jnp.isinf(grad), "Gradient should not be infinite."