diff --git a/src/gt4py/next/program_processors/runners/gtfn.py b/src/gt4py/next/program_processors/runners/gtfn.py
index c0a9be9168..f218d754e2 100644
--- a/src/gt4py/next/program_processors/runners/gtfn.py
+++ b/src/gt4py/next/program_processors/runners/gtfn.py
@@ -10,7 +10,7 @@
 import pathlib
 import tempfile
 import warnings
-from typing import Any, Optional
+from typing import Any, Callable, Optional
 
 import diskcache
 import factory
@@ -21,7 +21,8 @@
 from gt4py.eve import utils
 from gt4py.eve.utils import content_hash
 from gt4py.next import backend, common, config
-from gt4py.next.iterator import ir as itir
+from gt4py.next.embedded import nd_array_field
+from gt4py.next.iterator import embedded, ir as itir
 from gt4py.next.otf import arguments, recipes, stages, workflow
 from gt4py.next.otf.binding import nanobind
 from gt4py.next.otf.compilation import compiler
@@ -29,16 +30,71 @@
 from gt4py.next.program_processors.codegens.gtfn import gtfn_module
 
 
-# TODO(ricoh): Add support for the whole range of arguments that can be passed to a fencil.
-def convert_arg(arg: Any) -> Any:
-    if isinstance(arg, tuple):
-        return tuple(convert_arg(a) for a in arg)
-    if isinstance(arg, common.Field):
-        arr = arg.ndarray
-        origin = getattr(arg, "__gt_origin__", tuple([0] * len(arg.domain)))
-        return arr, origin
-    else:
-        return arg
+def handle_tuple(arg: Any, convert_arg: Callable) -> Any:
+    return tuple(convert_arg(a) for a in arg)
+
+
+def handle_field(arg: nd_array_field.NdArrayField) -> tuple:
+    arr = arg.ndarray
+    origin = getattr(arg, "__gt_origin__", tuple([0] * len(arg.domain)))
+    return arr, origin
+
+
+type_handlers_convert_args = {
+    tuple: handle_tuple,
+    nd_array_field.NumPyArrayField: handle_field,
+}
+
+ConnectivityArg = tuple[core_defs.NDArrayObject, tuple[int, ...]]
+
+
+def handle_neighbortable(
+    conn: embedded.NeighborTableOffsetProvider,  # type: ignore
+    zero_tuple: tuple[int, ...],
+    device: core_defs.DeviceType,
+) -> ConnectivityArg:
+    return (_ensure_is_on_device(conn.table, device), zero_tuple)  # type: ignore
+
+
+def handle_connectivity_field(
+    conn: nd_array_field.NdArrayField,
+    zero_tuple: tuple[int, ...],
+    device: core_defs.DeviceType,
+    copy: bool,
+) -> ConnectivityArg:
+    return (_ensure_is_on_device(conn.ndarray, device), zero_tuple)
+
+
+def handle_dimension(*args: Any, **kwargs: Any) -> None:
+    return None
+
+
+def handle_invalid_type(conn: Any, *args: Any, **kwargs: Any) -> None:
+    raise AssertionError(
+        f"Unsupported offset provider type '{type(conn).__name__}'. "
+        "Expected 'Connectivity' or 'Dimension'."
+    )
+
+
+type_handlers_connectivity_args = {
+    embedded.NeighborTableOffsetProvider: handle_neighbortable,
+    nd_array_field.NumPyArrayConnectivityField: handle_connectivity_field,
+    common.Dimension: handle_dimension,
+}
+
+try:
+    import cupy as cp
+
+    type_handlers_convert_args[nd_array_field.CuPyArrayField] = handle_field
+    type_handlers_connectivity_args[nd_array_field.CuPyArrayConnectivityField] = (
+        handle_connectivity_field
+    )
+except ImportError:
+    cp = None
+
+
+def handle_default(arg: Any) -> Any:
+    return arg
 
 
 def convert_args(
@@ -63,6 +119,14 @@ def decorated_program(
     return decorated_program
 
 
+def convert_arg(arg: Any) -> Any:
+    handler = type_handlers_convert_args.get(type(arg), handle_default)  # type: ignore
+    if handler is handle_tuple:
+        return handler(arg, convert_arg)
+    else:
+        return handler(arg)
+
+
 def _ensure_is_on_device(
     connectivity_arg: core_defs.NDArrayObject, device: core_defs.DeviceType
 ) -> core_defs.NDArrayObject:
@@ -79,26 +143,16 @@ def _ensure_is_on_device(
 
 
 def extract_connectivity_args(
-    offset_provider: dict[str, common.Connectivity | common.Dimension], device: core_defs.DeviceType
-) -> list[tuple[core_defs.NDArrayObject, tuple[int, ...]]]:
-    # note: the order here needs to agree with the order of the generated bindings
+    offset_provider: dict[str, common.Connectivity | common.Dimension],
+    device: core_defs.DeviceType,
+) -> list[ConnectivityArg]:
+    zero_tuple = (0, 0)
     args: list[tuple[core_defs.NDArrayObject, tuple[int, ...]]] = []
-    for name, conn in offset_provider.items():
-        if isinstance(conn, common.Connectivity):
-            if not common.is_neighbor_table(conn):
-                raise NotImplementedError(
-                    "Only 'NeighborTable' connectivities implemented at this point."
-                )
-            # copying to device here is a fallback for easy testing and might be removed later
-            conn_arg = _ensure_is_on_device(conn.ndarray, device)
-            args.append((conn_arg, tuple([0] * 2)))
-        elif isinstance(conn, common.Dimension):
-            pass
-        else:
-            raise AssertionError(
-                f"Expected offset provider '{name}' to be a 'Connectivity' or 'Dimension', "
-                f"but got '{type(conn).__name__}'."
-            )
+    for conn in offset_provider.values():
+        handler = type_handlers_connectivity_args.get(type(conn), handle_invalid_type)
+        result = handler(conn, zero_tuple, device)  # type: ignore
+        if result:
+            args.append(result)
     return args