diff --git a/phiml/math/_functional.py b/phiml/math/_functional.py
index 6a5cd237..375aba48 100644
--- a/phiml/math/_functional.py
+++ b/phiml/math/_functional.py
@@ -8,14 +8,14 @@
 import numpy as np
 
 from . import _ops as math, all_available
-from ._magic_ops import stack, pack_dims, expand, unpack_dim
+from ._magic_ops import stack, slice_
 from ._shape import EMPTY_SHAPE, Shape, spatial, instance, batch, channel, merge_shapes, DimFilter, shape
 from ._sparse import SparseCoordinateTensor
 from ._tensors import Tensor, disassemble_tree, assemble_tree, disassemble_tensors, assemble_tensors, variable_attributes, wrap, specs_equal, equality_by_shape_and_value
 from ._trace import ShiftLinTracer, matrix_from_function, LinearTraceInProgress
-from ..backend import Backend, NUMPY
-from ..backend._backend import get_spatial_derivative_order, functional_derivative_evaluation, ML_LOGGER
 from .magic import PhiTreeNode, Shapable
+from ..backend import Backend
+from ..backend._backend import get_spatial_derivative_order, functional_derivative_evaluation, ML_LOGGER
 from ..backend._dtype import DType
 
 X = TypeVar('X')
@@ -1180,12 +1180,13 @@ def map_(function, *args, dims: DimFilter = shape, range=range, unwrap_scalars=T
     sliceable_kwargs = {k: v for k, v in kwargs.items() if isinstance(v, Shapable)}
     extra_args = [v for v in args if not isinstance(v, Shapable)]
     extra_kwargs = {k: v for k, v in kwargs.items() if not isinstance(v, Shapable)}
-    dims = merge_shapes(*sliceable_args, *sliceable_kwargs.values()).only(dims)
+    dims = merge_shapes(*sliceable_args, *sliceable_kwargs.values(), allow_varying_sizes=True).only(dims)
+    assert dims.well_defined, f"All arguments must have consistent sizes for all mapped dimensions. Trying to map along {dims} but some have varying sizes (marked as None)."
     assert dims.volume > 0, f"map dims must have volume > 0 but got {dims}"
     results = []
     for _, idx in zip(range(dims.volume), dims.meshgrid()):
-        idx_args = [v[idx] for v in sliceable_args]
-        idx_kwargs = {k: v[idx] for k, v in sliceable_kwargs.items()}
+        idx_args = [slice_(v, idx) for v in sliceable_args]
+        idx_kwargs = {k: slice(v, idx) for k, v in sliceable_kwargs.items()}
         if unwrap_scalars:
             idx_args = [v.native() if isinstance(v, Tensor) and v.rank == 0 else v for v in idx_args]
             idx_kwargs = {k: v.native() if isinstance(v, Tensor) and v.rank == 0 else v for k, v in idx_kwargs.items()}