diff --git a/test/torchaudio_unittest/transforms/autograd_test_impl.py b/test/torchaudio_unittest/transforms/autograd_test_impl.py
index 57e9cacf96..fc9201d291 100644
--- a/test/torchaudio_unittest/transforms/autograd_test_impl.py
+++ b/test/torchaudio_unittest/transforms/autograd_test_impl.py
@@ -8,9 +8,20 @@
 from torchaudio_unittest.common_utils import (
     TestBaseMixin,
     get_whitenoise,
+    nested_params,
 )
 
 
+# TODO:
+# - replace T.Spectrogram
+# - generalize it
+# - move to common_utils
+def get_spectrogram(return_complex):
+    spectrogram = T.Spectrogram(return_complex=return_complex, power=None)
+    waveform = get_whitenoise(sample_rate=8000, duration=0.05, n_channels=2)
+    return spectrogram(waveform)
+
+
 class AutogradTestMixin(TestBaseMixin):
     def assert_grad(
             self,
@@ -23,8 +34,12 @@ def assert_grad(
 
         inputs_ = []
         for i in inputs:
-            i.requires_grad = True
-            inputs_.append(i.to(dtype=torch.float64, device=self.device))
+            if torch.is_tensor(i):
+                i = i.to(
+                    dtype=torch.cdouble if i.is_complex() else torch.double,
+                    device=self.device)
+                i.requires_grad = True
+            inputs_.append(i)
         assert gradcheck(transform, inputs_)
         assert gradgradcheck(transform, inputs_, nondet_tol=nondet_tol)
 
@@ -88,3 +103,21 @@ def test_fade(self, fade_shape):
         transform = T.Fade(fade_shape=fade_shape)
         waveform = get_whitenoise(sample_rate=8000, duration=0.05, n_channels=2)
         self.assert_grad(transform, [waveform], nondet_tol=1e-10)
+
+    @nested_params(
+        [0.7, 0.8, 0.9, 1.0, 1.3],
+        [True, False],
+    )
+    def test_timestretch(self, rate, test_complex):
+        transform = T.TimeStretch(fixed_rate=rate)
+        spectrogram = get_spectrogram(return_complex=test_complex)
+        self.assert_grad(transform, [spectrogram])
+
+    @nested_params(
+        [0.7, 0.8, 0.9, 1.0, 1.3],
+        [True, False],
+    )
+    def test_timestretch_override(self, rate, test_complex):
+        transform = T.TimeStretch()
+        spectrogram = get_spectrogram(return_complex=test_complex)
+        self.assert_grad(transform, [spectrogram, rate])