diff --git a/mlx/random.cpp b/mlx/random.cpp
index 1490be159..fae2e592c 100644
--- a/mlx/random.cpp
+++ b/mlx/random.cpp
@@ -90,6 +90,16 @@ T below_one() {
   return f;
 }
 
+// Get the next representable value above -1.0 for half precision
+// floating point types (fp16, bf16)
+template <typename T>
+T above_minus_one() {
+  T f = T(-1.0);
+  uint16_t* m = (uint16_t*)&f;
+  *m -= 1;
+  return f;
+}
+
 array uniform(
     const array& low,
     const array& high,
@@ -158,7 +168,17 @@ array normal(
     const std::optional<array>& key /*= nullopt */,
     StreamOrDevice s /* = {} */) {
   auto stream = to_stream(s);
-  auto low = array(std::nextafter(-1.0f, 0.0f), dtype);
+  auto get_low = [&dtype]() {
+    switch (dtype) {
+      case float16:
+        return array(above_minus_one<float16_t>(), dtype);
+      case bfloat16:
+        return array(above_minus_one<bfloat16_t>(), dtype);
+      default:
+        return array(std::nextafter(-1.0f, 0.0f), dtype);
+    }
+  };
+  auto low = get_low();
   auto high = array(1.0f, dtype);
   auto samples = uniform(low, high, shape, dtype, key, stream);
   samples =
diff --git a/python/tests/test_random.py b/python/tests/test_random.py
index 892db37df..7515cf468 100644
--- a/python/tests/test_random.py
+++ b/python/tests/test_random.py
@@ -96,6 +96,11 @@ class TestRandom(mlx_tests.MLXTestCase):
 
         self.assertEqual(mx.random.normal().dtype, mx.random.normal(dtype=None).dtype)
 
+        # Test not getting -inf or inf with half precison
+        for hp in [mx.float16, mx.bfloat16]:
+            a = abs(mx.random.normal(shape=(10000,), loc=0, scale=1, dtype=hp))
+            self.assertTrue(mx.all(a < mx.inf))
+
     def test_randint(self):
         a = mx.random.randint(0, 1, [])
         self.assertEqual(a.shape, ())