diff --git a/src/torchmetrics/functional/image/ssim.py b/src/torchmetrics/functional/image/ssim.py
index e43a91f2466..77c23a9872c 100644
--- a/src/torchmetrics/functional/image/ssim.py
+++ b/src/torchmetrics/functional/image/ssim.py
@@ -160,8 +160,8 @@ def _ssim_update(
     sigma_target_sq = output_list[3] - mu_target_sq
     sigma_pred_target = output_list[4] - mu_pred_target
 
-    upper = 2 * sigma_pred_target + c2
-    lower = sigma_pred_sq + sigma_target_sq + c2
+    upper = 2 * sigma_pred_target.to(dtype) + c2
+    lower = (sigma_pred_sq + sigma_target_sq).to(dtype) + c2
 
     ssim_idx_full_image = ((2 * mu_pred_target + c1) * upper) / ((mu_pred_sq + mu_target_sq + c1) * lower)