diff --git a/CHANGELOG.md b/CHANGELOG.md
index 425fabb..661e5c4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,10 @@
 
 ## Unreleased
 
+### Added
+
+- GridInterpolation transformation for xarray-esque rectilinear grids
+
 ## 0.7.2 - 2026-06-25
 
 ## 0.7.1 - 2026-06-25
diff --git a/README.md b/README.md
index 4149a31..c2568d9 100644
--- a/README.md
+++ b/README.md
@@ -42,7 +42,9 @@ All transforms are accessed under the `transformnd.transforms` subpackage.
 | `Scale` | | Multiply the input coordinates by constant scale factor |
 | `Reflection` | | Reflect coordinates about arbitrary planes |
 | `MapAxis` | | Rearrange axes of the input coordinates |
+| `ProjectAxis` | | Insert or remove axes |
 | `Affine` | | Multiply augmented coordinates by an affine transformation matrix. Can represent all of the above transformations. Can be composed with matrix multiplication `aff2 @ aff1`. |
+| `GridInterpolation` | | Apply an arbitrary callable (e.g. a `scipy.interpolate` interpolator) to each dimension. |
 | `ByDimension` | | Apply different transformations to subsets of the input coordinates' dimensions |
 | `MovingLeastSquares` | `movingleastsquares` | Landmark-based transformation. |
 | `ThinPlateSplines` | `thinplatesplines` | Landmark-based transformation. |
diff --git a/src/transformnd/transforms/__init__.py b/src/transformnd/transforms/__init__.py
index 37de554..e3f8500 100644
--- a/src/transformnd/transforms/__init__.py
+++ b/src/transformnd/transforms/__init__.py
@@ -10,12 +10,14 @@
 from .vector_field import Coordinates, Displacements
 from .moving_least_squares import MovingLeastSquares
 from .thinplate import ThinPlateSplines
+from .grid import GridInterpolation
 
 __all__ = [
     "Affine",
     "Identity",
     "ProjectAxis",
     "Reflect",
+    "GridInterpolation",
     "Scale",
     "Translate",
     "MapAxis",
diff --git a/src/transformnd/transforms/grid.py b/src/transformnd/transforms/grid.py
new file mode 100644
index 0000000..99f82f7
--- /dev/null
+++ b/src/transformnd/transforms/grid.py
@@ -0,0 +1,47 @@
+from typing import Any, Protocol, Generic
+
+from array_api_compat import array_namespace
+from transformnd.types import NDims, Spaces
+from ..base import Transform
+from ..types import ArrayT
+
+
+class Interpolator(Protocol, Generic[ArrayT]):
+    def __call__(self, x: ArrayT) -> ArrayT: ...
+
+
+class GridInterpolation(Transform[ArrayT]):
+    """Coordinate transformation which applies a callable to each dimension.
+
+    Intended for use with instances of `scipy.interpolate` interpolators,
+    but any callable which takes and returns an array of floats would work.
+    """
+
+    def __init__(
+        self,
+        interpolators: list[Interpolator[ArrayT]],
+        *,
+        spaces: Spaces = Spaces(None, None),
+    ):
+        """
+        Parameters
+        ----------
+        interpolators
+            One callable per dimension, in order.
+            Each one should take and return an array of floats.
+        spaces
+            Source and target space identifiers
+        """
+        self.interpolators = interpolators
+        nd = len(interpolators)
+        super().__init__(NDims(nd, nd), spaces=spaces)
+
+    def apply(self, coords: Any) -> Any:
+        xp = array_namespace(coords)
+        coords = self._validate_coords(coords)
+        coords_t = xp.transpose(coords)
+        out_coords_t = xp.zeros_like(coords_t)
+        for in_col, out_col, interp in zip(coords_t, out_coords_t, self.interpolators):
+            out_col[:] = interp(in_col)
+
+        return xp.transpose(out_coords_t)
diff --git a/tests/transforms/test_grid.py b/tests/transforms/test_grid.py
new file mode 100644
index 0000000..08baf08
--- /dev/null
+++ b/tests/transforms/test_grid.py
@@ -0,0 +1,8 @@
+from transformnd.transforms import GridInterpolation
+import pytest
+
+
+def test_simple(coords5x3):
+    t = GridInterpolation([lambda x: x * 2, lambda x: x * 3, lambda x: x * 4])
+    out = t.apply(coords5x3)
+    assert out == pytest.approx(coords5x3 * [2, 3, 4])