diff --git a/mlx/random.cpp b/mlx/random.cpp
index 5367e7ca9..65ea60535 100644
--- a/mlx/random.cpp
+++ b/mlx/random.cpp
@@ -82,39 +82,6 @@ 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;
-}
-
-// 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;
-}
-
-// Get the next representable value above -1.0 for half precision
-// use std::nextafter as default case.
-array above_minus_one_with_default(Dtype 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);
-  }
-}
-
 array uniform(
     const array& low,
     const array& high,
@@ -139,31 +106,11 @@ array uniform(
         << " from broadcasted shape " << out_shape << ".";
     throw std::invalid_argument(msg.str());
   }
-  // Get random values between [0, nextafter(maxval, 0.0f)] since samples must
-  // be in [low, high)
-  auto get_limits = [&dtype]() {
-    switch (dtype) {
-      case float32:
-        return std::make_pair(
-            array(std::nextafter(1.0f, 0.0f), float32),
-            array(std::numeric_limits<uint32_t>::max(), float32));
-      case float16:
-        return std::make_pair(
-            array(below_one<float16_t>(), float16),
-            array(std::numeric_limits<uint32_t>::max(), float32));
-      case bfloat16:
-        return std::make_pair(
-            array(below_one<bfloat16_t>(), bfloat16),
-            array(std::numeric_limits<uint16_t>::max(), bfloat16));
-      default:
-        throw std::runtime_error("[uniform] Unsupported type.");
-    }
-  };
-
-  auto [upper, maxval] = get_limits();
-  auto out = bits(shape, size_of(maxval.dtype()), key, stream);
-  out = astype(divide(out, maxval, stream), dtype, stream);
-  out = minimum(out, upper, stream);
+  auto upper = array(std::nextafter(1.0f, 0.0f), float32);
+  auto maxval = array(std::numeric_limits<uint32_t>::max(), float32);
+  auto out = bits(shape, size_of(float32), key, stream);
+  out = divide(out, maxval, stream);
+  out = astype(minimum(out, upper, stream), dtype, stream);
   return add(multiply(range, out, stream), lo, stream);
 }
 
@@ -183,7 +130,7 @@ inline array complex_normal(
     const std::optional<array>& key,
     StreamOrDevice s) {
   auto stream = to_stream(s);
-  auto low = above_minus_one_with_default(float32);
+  auto low = array(std::nextafter(-1.0f, 0.0f), float32);
   auto high = array(1.0f, float32);
   shape.push_back(2);
   auto samples =
@@ -210,15 +157,16 @@ array normal(
   }
 
   auto stream = to_stream(s);
-  auto low = above_minus_one_with_default(dtype);
-  auto high = array(1.0f, dtype);
-  auto samples = uniform(low, high, shape, dtype, key, stream);
+  auto low = array(std::nextafter(-1.0f, 0.0f), float32);
+  auto high = array(1.0f, float32);
+  auto samples = uniform(low, high, shape, float32, key, stream);
   auto applied_scale = array(std::sqrt(2.0), dtype);
   if (scale.has_value()) {
     applied_scale =
         multiply(applied_scale, astype(*scale, dtype, stream), stream);
   }
-  samples = multiply(applied_scale, erfinv(samples, stream), stream);
+  samples = astype(erfinv(samples, stream), dtype, stream);
+  samples = multiply(applied_scale, samples, stream);
   if (loc.has_value()) {
     samples = add(astype(*loc, dtype, stream), samples, stream);
   }
@@ -470,15 +418,16 @@ array laplace(
     const std::optional<array>& key /*= nullopt */,
     StreamOrDevice s /* = {} */) {
   auto stream = to_stream(s);
-  auto low = above_minus_one_with_default(dtype);
-  auto high = array(1.0f, dtype);
-  auto samples = uniform(low, high, shape, dtype, key, stream);
+  auto low = array(std::nextafter(-1.0f, 0.0f), float32);
+  auto high = array(1.0f, float32);
+  auto samples = uniform(low, high, shape, float32, key, stream);
   // Use inverse CDF to generate Laplacian noise
   samples = multiply(
       sign(samples, stream),
       log1p(
           multiply(array(-1.0f, dtype), abs(samples, stream), stream), stream),
       stream);
+  samples = astype(samples, dtype, stream);
 
   if (scale != 1.0) {
     samples = multiply(array(scale, dtype), samples, stream);