diff --git a/gmmx/fit.py b/gmmx/fit.py
index 70daea1..c17357f 100644
--- a/gmmx/fit.py
+++ b/gmmx/fit.py
@@ -100,7 +100,12 @@ def m_step(
             Updated Gaussian mixture model instance.
         """
         x = jnp.expand_dims(x, axis=(Axis.components, Axis.features_covar))
-        return gmm.from_responsibilities(x, jnp.exp(log_resp), reg_covar=self.reg_covar)
+        return gmm.from_responsibilities(
+            x,
+            jnp.exp(log_resp),
+            reg_covar=self.reg_covar,
+            covariance_type=gmm.covariances.type,
+        )
 
     @jax.jit
     def fit(self, x: jax.Array, gmm: GaussianMixtureModelJax) -> EMFitterResult:
diff --git a/gmmx/gmm.py b/gmmx/gmm.py
index 23e4497..83a4502 100644
--- a/gmmx/gmm.py
+++ b/gmmx/gmm.py
@@ -51,7 +51,7 @@
 from dataclasses import dataclass
 from enum import Enum
 from functools import partial
-from typing import Any, Union
+from typing import Any, ClassVar, Union
 
 import jax
 import numpy as np
@@ -109,6 +109,7 @@ class FullCovariances:
     """
 
     values: jax.Array
+    type: ClassVar[CovarianceType] = CovarianceType.full
 
     def __post_init__(self) -> None:
         check_shape(self.values, (1, None, None, None))
@@ -273,7 +274,7 @@ def precisions_cholesky(self) -> jax.Array:
 
 
 COVARIANCE: dict[CovarianceType, Any] = {
-    CovarianceType.full: FullCovariances,
+    FullCovariances.type: FullCovariances,
 }
 
 # keep this mapping separate, as names in sklearn might change