diff --git a/CHANGELOG.md b/CHANGELOG.md
index 18840193b2e..894903f48a8 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -46,6 +46,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fixed JaccardIndex multi-label compute ([#1125](https://github.com/Lightning-AI/metrics/pull/1125))
 
 
+- Fix SSIM propagate device if `gaussian_kernel` is False, add test ([#1149](https://github.com/Lightning-AI/metrics/pull/1149))
+
+
 
 ## [0.9.2] - 2022-06-29
 
diff --git a/tests/image/test_ssim.py b/tests/image/test_ssim.py
index e868fe96570..daed5445a30 100644
--- a/tests/image/test_ssim.py
+++ b/tests/image/test_ssim.py
@@ -125,6 +125,23 @@ def test_ssim(self, preds, target, sigma, ddp, dist_sync_on_step):
             dist_sync_on_step=dist_sync_on_step,
         )
 
+    @pytest.mark.parametrize("ddp", [True, False])
+    @pytest.mark.parametrize("dist_sync_on_step", [True, False])
+    def test_ssim_without_gaussian_kernel(self, preds, target, sigma, ddp, dist_sync_on_step):
+        self.run_class_metric_test(
+            ddp,
+            preds,
+            target,
+            StructuralSimilarityIndexMeasure,
+            partial(_sk_ssim, data_range=1.0, sigma=sigma, kernel_size=None),
+            metric_args={
+                "gaussian_kernel": False,
+                "data_range": 1.0,
+                "sigma": sigma,
+            },
+            dist_sync_on_step=dist_sync_on_step,
+        )
+
     def test_ssim_functional(self, preds, target, sigma):
         self.run_functional_metric_test(
             preds,
diff --git a/torchmetrics/functional/image/ssim.py b/torchmetrics/functional/image/ssim.py
index 2c775994018..57636469867 100644
--- a/torchmetrics/functional/image/ssim.py
+++ b/torchmetrics/functional/image/ssim.py
@@ -150,7 +150,9 @@ def _ssim_compute(
             kernel = _gaussian_kernel_2d(channel, gauss_kernel_size, sigma, dtype, device)
 
     if not gaussian_kernel:
-        kernel = torch.ones((1, 1, *kernel_size)) / torch.prod(Tensor(kernel_size))
+        kernel = torch.ones((channel, 1, *kernel_size), dtype=dtype, device=device) / torch.prod(
+            torch.tensor(kernel_size, dtype=dtype, device=device)
+        )
 
     input_list = torch.cat((preds, target, preds * preds, target * target, preds * target))  # (5 * B, C, H, W)