diff --git a/torch/distributions/wishart.py b/torch/distributions/wishart.py
index af049724f43..9cc3c411d1b 100644
--- a/torch/distributions/wishart.py
+++ b/torch/distributions/wishart.py
@@ -277,16 +277,8 @@ class Wishart(ExponentialFamily):
 
     @property
     def _natural_params(self):
-        nu = self.df  # has shape (batch_shape)
-        p = self._event_shape[-1]  # has singleton shape
-        return (
-            - 0.5 * self.precision_matrix,
-            0.5 * nu,
-        )
+        return self.precision_matrix, self.df
 
     def _log_normalizer(self, x, y):
         p = self._event_shape[-1]
-        return (
-            y * (- torch.linalg.slogdet(-2 * x).logabsdet + _log_2 * p)
-            + torch.mvlgamma(y, p=p)
-        )
+        return 0.5 * y * (- torch.linalg.slogdet(-x).logabsdet + _log_2 * p) + torch.mvlgamma(y, p=p)