diff --git a/tests/ignite/metrics/test_ssim.py b/tests/ignite/metrics/test_ssim.py
index b158c181e79b..3c77dda13f56 100644
--- a/tests/ignite/metrics/test_ssim.py
+++ b/tests/ignite/metrics/test_ssim.py
@@ -1,5 +1,6 @@
 import os
 
+import numpy as np
 import pytest
 import torch
 
@@ -20,14 +21,14 @@ def test_zero_div():
 
 
 def test_invalid_ssim():
-    y_pred = torch.rand(16, 1, 32, 32)
+    y_pred = torch.rand(1, 1, 4, 4)
     y = y_pred + 0.125
-    with pytest.raises(ValueError, match=r"Expected kernel_size to have odd positive number. Got 10."):
-        ssim = SSIM(data_range=1.0, kernel_size=10)
+    with pytest.raises(ValueError, match=r"Expected kernel_size to have odd positive number."):
+        ssim = SSIM(data_range=1.0, kernel_size=2)
         ssim.update((y_pred, y))
         ssim.compute()
 
-    with pytest.raises(ValueError, match=r"Expected kernel_size to have odd positive number. Got -1."):
+    with pytest.raises(ValueError, match=r"Expected kernel_size to have odd positive number."):
         ssim = SSIM(data_range=1.0, kernel_size=-1)
         ssim.update((y_pred, y))
         ssim.compute()
@@ -42,38 +43,73 @@ def test_invalid_ssim():
         ssim.update((y_pred, y))
         ssim.compute()
 
+    with pytest.raises(ValueError, match=r"Expected sigma to have positive number."):
+        ssim = SSIM(data_range=1.0, sigma=(-1, -1))
+        ssim.update((y_pred, y))
+        ssim.compute()
+
     with pytest.raises(ValueError, match=r"Argument sigma should be either float or a sequence of float."):
         ssim = SSIM(data_range=1.0, sigma=1)
         ssim.update((y_pred, y))
         ssim.compute()
 
+    with pytest.raises(ValueError, match=r"Expected y_pred and y to have the same shape."):
+        y = y.squeeze(dim=0)
+        ssim = SSIM(data_range=1.0)
+        ssim.update((y_pred, y))
+        ssim.compute()
 
-def test_ssim():
-    device = "cuda" if torch.cuda.is_available() else "cpu"
-    ssim = SSIM(data_range=1.0, device=device)
-    y_pred = torch.rand(16, 3, 64, 64, device=device)
-    y = y_pred * 0.65
-    ssim.update((y_pred, y))
+    with pytest.raises(ValueError, match=r"Expected y_pred and y to have BxCxHxW shape."):
+        y = y.squeeze(dim=0)
+        ssim = SSIM(data_range=1.0)
+        ssim.update((y, y))
+        ssim.compute()
 
-    np_pred = y_pred.permute(0, 2, 3, 1).cpu().numpy()
-    np_y = np_pred * 0.65
-    np_ssim = ski_ssim(np_pred, np_y, win_size=11, multichannel=True, gaussian_weights=True, data_range=1.0)
+    with pytest.raises(TypeError, match=r"Expected y_pred and y to have the same data type."):
+        y = y.double()
+        ssim = SSIM(data_range=1.0)
+        ssim.update((y_pred, y))
+        ssim.compute()
 
-    assert isinstance(ssim.compute(), torch.Tensor)
-    assert torch.allclose(ssim.compute(), torch.tensor(np_ssim, dtype=torch.float64, device=device), atol=1e-4)
 
-    device = "cuda" if torch.cuda.is_available() else "cpu"
-    ssim = SSIM(data_range=1.0, gaussian=False, kernel_size=7, device=device)
-    y_pred = torch.rand(16, 3, 227, 227, device=device)
-    y = y_pred * 0.65
+def _test_ssim(y_pred, y, data_range, kernel_size, sigma, gaussian, use_sample_covariance, device):
+    atol = 7e-5
+    ssim = SSIM(data_range=data_range, sigma=sigma, device=device)
     ssim.update((y_pred, y))
+    ignite_ssim = ssim.compute()
+
+    skimg_pred = y_pred.permute(0, 2, 3, 1).cpu().numpy()
+    skimg_y = skimg_pred * 0.8
+    skimg_ssim = ski_ssim(
+        skimg_pred,
+        skimg_y,
+        win_size=kernel_size,
+        sigma=sigma,
+        multichannel=True,
+        gaussian_weights=gaussian,
+        data_range=data_range,
+        use_sample_covariance=use_sample_covariance,
+    )
+
+    assert isinstance(ignite_ssim, torch.Tensor)
+    assert ignite_ssim.dtype == torch.float64
+    assert ignite_ssim.device == torch.device(device)
+    assert np.allclose(ignite_ssim.numpy(), skimg_ssim, atol=atol)
 
-    np_pred = y_pred.permute(0, 2, 3, 1).cpu().numpy()
-    np_y = np_pred * 0.65
-    np_ssim = ski_ssim(np_pred, np_y, win_size=7, multichannel=True, gaussian_weights=False, data_range=1.0)
 
-    assert isinstance(ssim.compute(), torch.Tensor)
-    assert torch.allclose(ssim.compute(), torch.tensor(np_ssim, dtype=torch.float64, device=device), atol=1e-4)
+def test_ssim():
+    device = "cuda" if torch.cuda.is_available() else "cpu"
+    y_pred = torch.rand(8, 3, 224, 224, device=device)
+    y = y_pred * 0.8
+    _test_ssim(
+        y_pred, y, data_range=1.0, kernel_size=7, sigma=1.5, gaussian=False, use_sample_covariance=True, device=device
+    )
+
+    y_pred = torch.rand(12, 3, 28, 28, device=device)
+    y = y_pred * 0.8
+    _test_ssim(
+        y_pred, y, data_range=1.0, kernel_size=11, sigma=1.5, gaussian=True, use_sample_covariance=False, device=device
+    )
 
 
 def _test_distrib_integration(device, tol=1e-4):
@@ -105,7 +141,16 @@ def update(engine, i):
 
         np_pred = y_pred.permute(0, 2, 3, 1).cpu().numpy()
         np_true = np_pred * 0.65
-        true_res = ski_ssim(np_pred, np_true, win_size=11, multichannel=True, gaussian_weights=True, data_range=1.0)
+        true_res = ski_ssim(
+            np_pred,
+            np_true,
+            win_size=11,
+            sigma=1.5,
+            multichannel=True,
+            gaussian_weights=True,
+            data_range=1.0,
+            use_sample_covariance=False,
+        )
 
         assert pytest.approx(res, abs=tol) == true_res
 
@@ -142,7 +187,7 @@ def _test_distrib_accumulator_device(device):
             type(ssim._kernel.device), ssim._kernel.device, type(metric_device), metric_device
         )
 
-        y_pred = torch.rand(4, 3, 28, 28, dtype=torch.float, device=device)
+        y_pred = torch.rand(2, 3, 28, 28, dtype=torch.float, device=device)
         y = y_pred * 0.65
         ssim.update((y_pred, y))