diff --git a/aten/src/ATen/test/cuda_stream_test.cpp b/aten/src/ATen/test/cuda_stream_test.cpp
index a1944ca4422e..dfd823f27349 100644
--- a/aten/src/ATen/test/cuda_stream_test.cpp
+++ b/aten/src/ATen/test/cuda_stream_test.cpp
@@ -69,6 +69,24 @@ TEST(TestStream, CopyAndMoveTest) {
   ASSERT_EQ_CUDA(moveStream.stream(), cuda_stream);
 }
 
+// Verifies stream priority is handled properly
+TEST(TestStream, StreamPriorityTest) {
+  if (!at::cuda::is_available()) return;
+  auto [least_priority, greatest_priority] =
+      at::cuda::CUDAStream::priority_range();
+  EXPECT_EQ(least_priority, 0);
+
+  auto stream = at::cuda::getStreamFromPool(-1);
+  EXPECT_EQ(stream.priority(), -1);
+  EXPECT_GT(10, at::cuda::max_compile_time_stream_priorities);
+  stream = at::cuda::getStreamFromPool(-10);
+  EXPECT_EQ(stream.priority(), greatest_priority);
+  stream = at::cuda::getStreamFromPool(0);
+  EXPECT_EQ(stream.priority(), 0);
+  stream = at::cuda::getStreamFromPool(10);
+  EXPECT_EQ(stream.priority(), 0);
+}
+
 // Verifies streams are set properly
 TEST(TestStream, GetAndSetTest) {
   if (!at::cuda::is_available()) return;
diff --git a/c10/cuda/CUDAStream.cpp b/c10/cuda/CUDAStream.cpp
index 23ab4a7f6edc..bbaeeba84ddc 100644
--- a/c10/cuda/CUDAStream.cpp
+++ b/c10/cuda/CUDAStream.cpp
@@ -318,10 +318,6 @@ CUDAStream getStreamFromPool(const int priority, DeviceIndex device_index) {
     device_index = current_device();
     c10::cuda::SetTargetDevice();
   }
-  TORCH_CHECK(
-      priority <= 0,
-      "Expected cuda stream priority to be less than or equal to 0, got ",
-      priority);
   check_gpu(device_index);
 #if !defined(USE_ROCM)
   // See Note [HIP Lazy Streams]
@@ -329,9 +325,7 @@ CUDAStream getStreamFromPool(const int priority, DeviceIndex device_index) {
   c10::call_once(
       device_flags[device_index], initDeviceStreamState, device_index);
 #endif
-  auto pri_idx = -priority;
-  pri_idx =
-      std::min(pri_idx, max_stream_priorities - 1); // pri_idx is zero-based
+  auto pri_idx = std::clamp(-priority, 0, max_stream_priorities - 1);
   const auto idx = get_idx(priority_counters[pri_idx][device_index]);
   StreamIdType id_type = StreamIdType(pri_idx + 1);
   return CUDAStreamForId(device_index, makeStreamId(id_type, idx));
diff --git a/torch/cuda/streams.py b/torch/cuda/streams.py
index 6ef0baeeaf4e..cefe9caf9cda 100644
--- a/torch/cuda/streams.py
+++ b/torch/cuda/streams.py
@@ -22,9 +22,11 @@ class Stream(torch._C._CudaStreamBase):
         device(torch.device or int, optional): a device on which to allocate
             the stream. If :attr:`device` is ``None`` (default) or a negative
             integer, this will use the current device.
-        priority(int, optional): priority of the stream, should be 0 or
-            negative, where negative numbers indicate higher priority. By default,
-            streams have priority 0.
+        priority(int, optional): priority of the stream, which can be positive, 0, or negative.
+            A lower number indicates a higher priority. By default, the priority is set to 0.
+            If the value falls outside of the allowed priority range, it will automatically be
+            mapped to the nearest valid priority (lowest for large positive numbers or
+            highest for large negative numbers).
 
     """