diff --git a/nitransforms/nonlinear.py b/nitransforms/nonlinear.py
index 1f5b14f..0cb40f3 100644
--- a/nitransforms/nonlinear.py
+++ b/nitransforms/nonlinear.py
@@ -36,9 +36,9 @@
 class DenseFieldTransform(TransformBase):
     """Represents dense field (voxel-wise) transforms."""
 
-    __slots__ = ("_field", "_deltas", "_is_deltas")
+    __slots__ = ("_field", "_deltas", "_is_deltas", "_filtered_field")
 
-    def __init__(self, field=None, is_deltas=True, reference=None):
+    def __init__(self, field=None, is_deltas=True, reference=None, do_prefilter=True):
         """
         Create a dense field transform.
 
@@ -107,6 +107,17 @@ def __init__(self, field=None, is_deltas=True, reference=None):
         else:
             self._field = _data.copy()
 
+        self._filtered_field = None
+        if do_prefilter:
+            # pre-cache filtered field to accelerate later mapping
+            from scipy.ndimage import spline_filter
+            for i in range(self.reference.ndim):
+                filtered_field_i = spline_filter(self._field[..., i], order=3, output=np.float64, mode='constant')
+                if self._filtered_field is None:
+                    self._filtered_field = np.repeat(filtered_field_i[..., np.newaxis], self.reference.ndim, axis=-1)
+                else:
+                    self._filtered_field[..., i] = filtered_field_i
+
     def __repr__(self):
         """Beautify the python representation."""
         return f"<{self.__class__.__name__}[{self._field.shape[-1]}D] {self._field.shape[:3]}>"
@@ -193,12 +204,12 @@ def map(self, x, inverse=False):
         mapped_coords = np.vstack(
             tuple(
                 map_coordinates(
-                    self._field[..., i],
+                    self._field[..., i] if self._filtered_field is None else self._filtered_field[..., i],
                     ijk.T,
                     order=3,
                     mode="constant",
                     cval=np.nan,
-                    prefilter=True,
+                    prefilter=self._filtered_field is None,
                 )
                 for i in range(self.reference.ndim)
             )