diff --git a/mlx/random.cpp b/mlx/random.cpp
index 65ea60535..def3169cb 100644
--- a/mlx/random.cpp
+++ b/mlx/random.cpp
@@ -82,6 +82,16 @@ array split(const array& key, int num, StreamOrDevice s /* = {} */) {
   return bits({num, 2}, 4, key, s);
 }
 
+// Get the next representable value below 1.0 for half precision
+// floating point types (fp16, bf16)
+template <typename T>
+T below_one() {
+  T f = T(1.0);
+  uint16_t* m = (uint16_t*)&f;
+  *m -= 1;
+  return f;
+}
+
 array uniform(
     const array& low,
     const array& high,
@@ -106,7 +116,23 @@ array uniform(
         << " from broadcasted shape " << out_shape << ".";
     throw std::invalid_argument(msg.str());
   }
-  auto upper = array(std::nextafter(1.0f, 0.0f), float32);
+
+  // Get random values between [0, nextafter(1.0, 0.0)] since samples must
+  // be in [low, high)
+  auto get_upper = [&dtype]() {
+    switch (dtype) {
+      case float32:
+        return array(std::nextafter(1.0f, 0.0f), float32);
+      case float16:
+        return array(below_one<float16_t>(), float32);
+      case bfloat16:
+        return array(below_one<bfloat16_t>(), float32);
+      default:
+        throw std::runtime_error("[uniform] Unsupported type.");
+    }
+  };
+
+  auto upper = get_upper();
   auto maxval = array(std::numeric_limits<uint32_t>::max(), float32);
   auto out = bits(shape, size_of(float32), key, stream);
   out = divide(out, maxval, stream);
@@ -154,6 +180,10 @@ array normal(
     StreamOrDevice s /* = {} */) {
   if (dtype == complex64) {
     return complex_normal(shape, loc, scale, key, s);
+  } else if (!issubdtype(dtype, floating)) {
+    throw std::invalid_argument(
+        "[normal] Can only generate uniform numbers with "
+        "floating point type.");
   }
 
   auto stream = to_stream(s);
@@ -417,6 +447,12 @@ array laplace(
     const float scale /* = 1.0 */,
     const std::optional<array>& key /*= nullopt */,
     StreamOrDevice s /* = {} */) {
+  if (!issubdtype(dtype, floating)) {
+    throw std::invalid_argument(
+        "[laplace] Can only generate uniform numbers with real"
+        "floating point type.");
+  }
+
   auto stream = to_stream(s);
   auto low = array(std::nextafter(-1.0f, 0.0f), float32);
   auto high = array(1.0f, float32);
diff --git a/tests/random_tests.cpp b/tests/random_tests.cpp
index 49f1f300b..6ddd37104 100644
--- a/tests/random_tests.cpp
+++ b/tests/random_tests.cpp
@@ -350,7 +350,7 @@ TEST_CASE("test random uniform") {
   // Check float16
   {
     auto key = random::key(0);
-    auto out = random::uniform({100}, float16, key);
+    auto out = random::uniform({1000}, float16, key);
     CHECK_EQ(out.dtype(), float16);
     CHECK(all(less(out, array(1.0f))).item<bool>());
     CHECK(all(greater_equal(out, array(0.0f))).item<bool>());
@@ -360,7 +360,7 @@ TEST_CASE("test random uniform") {
 
   {
     auto key = random::key(0);
-    auto out = random::uniform({100}, bfloat16, key);
+    auto out = random::uniform({1000}, bfloat16, key);
     CHECK_EQ(out.dtype(), bfloat16);
     CHECK(all(less(out, array(1.0f))).item<bool>());
     CHECK(all(greater_equal(out, array(0.0f))).item<bool>());