diff --git a/src/moscot/backends/ott/_utils.py b/src/moscot/backends/ott/_utils.py
index fc623ac8e..1ed7a0cc8 100644
--- a/src/moscot/backends/ott/_utils.py
+++ b/src/moscot/backends/ott/_utils.py
@@ -1,6 +1,7 @@
 from typing import Any, Literal, Optional, Tuple, Union
 
 import jax
+import jax.experimental.sparse as jesp
 import jax.numpy as jnp
 import scipy.sparse as sp
 from ott.geometry import epsilon_scheduler, geodesic, geometry, pointcloud
@@ -67,6 +68,25 @@ def alpha_to_fused_penalty(alpha: float) -> float:
     return (1 - alpha) / alpha
 
 
+def densify(arr: ArrayLike) -> jax.Array:
+    """If the input is sparse, convert it t dense.
+
+    Parameters
+    ----------
+    arr
+        Array to check.
+
+    Returns
+    -------
+    dense :mod:`jax` array.
+    """
+    if sp.issparse(arr):
+        arr = arr.A  # type: ignore[attr-defined]
+    elif isinstance(arr, jesp.BCOO):
+        arr = arr.todense()
+    return jnp.asarray(arr)
+
+
 def ensure_2d(arr: ArrayLike, *, reshape: bool = False) -> jax.Array:
     """Ensure that an array is 2-dimensional.
 
@@ -81,9 +101,6 @@ def ensure_2d(arr: ArrayLike, *, reshape: bool = False) -> jax.Array:
     -------
     2-dimensional :mod:`jax` array.
     """
-    if sp.issparse(arr):
-        arr = arr.A  # type: ignore[attr-defined]
-    arr = jnp.asarray(arr)
     if reshape and arr.ndim == 1:
         return jnp.reshape(arr, (-1, 1))
     if arr.ndim != 2:
@@ -91,6 +108,13 @@ def ensure_2d(arr: ArrayLike, *, reshape: bool = False) -> jax.Array:
     return arr
 
 
+def convert_scipy_sparse(arr: Union[sp.spmatrix, jesp.BCOO]) -> jesp.BCOO:
+    """ If the input is a scipy sparse matrix, convert it to a jax BCOO."""
+    if sp.issparse(arr):
+        return jesp.BCOO.from_scipy_sparse(arr)
+    return arr
+
+
 def _instantiate_geodesic_cost(
     arr: jax.Array,
     problem_shape: Tuple[int, int],
diff --git a/src/moscot/backends/ott/solver.py b/src/moscot/backends/ott/solver.py
index f8130eab2..9d280d892 100644
--- a/src/moscot/backends/ott/solver.py
+++ b/src/moscot/backends/ott/solver.py
@@ -16,6 +16,8 @@
     _instantiate_geodesic_cost,
     alpha_to_fused_penalty,
     check_shapes,
+    convert_scipy_sparse,
+    densify,
     ensure_2d,
 )
 from moscot.backends.ott.output import GraphOTTOutput, OTTOutput
@@ -76,8 +78,8 @@ def _create_geometry(
             if not isinstance(cost_fn, costs.CostFn):
                 raise TypeError(f"Expected `cost_fn` to be `ott.geometry.costs.CostFn`, found `{type(cost_fn)}`.")
 
-            y = None if x.data_tgt is None else ensure_2d(x.data_tgt, reshape=True)
-            x = ensure_2d(x.data_src, reshape=True)
+            y = None if x.data_tgt is None else densify(ensure_2d(x.data_tgt, reshape=True))
+            x = densify(ensure_2d(x.data_src, reshape=True))
             if y is not None and x.shape[1] != y.shape[1]:
                 raise ValueError(
                     f"Expected `x/y` to have the same number of dimensions, found `{x.shape[1]}/{y.shape[1]}`."
@@ -94,6 +96,8 @@ def _create_geometry(
             )
 
         arr = ensure_2d(x.data_src, reshape=False)
+        arr = densify(arr) if x.is_graph else convert_scipy_sparse(arr)
+
         if x.is_cost_matrix:
             return geometry.Geometry(
                 cost_matrix=arr, epsilon=epsilon, relative_epsilon=relative_epsilon, scale_cost=scale_cost
diff --git a/tests/backends/ott/test_backend_utils.py b/tests/backends/ott/test_backend_utils.py
new file mode 100644
index 000000000..394d77038
--- /dev/null
+++ b/tests/backends/ott/test_backend_utils.py
@@ -0,0 +1,53 @@
+from typing import Optional, Tuple, Type, Union
+
+import pytest
+
+import jax
+import jax.numpy as jnp
+import numpy as np
+from ott.geometry import costs
+from ott.geometry.geometry import Geometry
+from ott.geometry.low_rank import LRCGeometry
+from ott.geometry.pointcloud import PointCloud
+from ott.problems.linear.linear_problem import LinearProblem
+from ott.problems.quadratic import quadratic_problem
+from ott.problems.quadratic.quadratic_problem import QuadraticProblem
+from ott.solvers.linear import solve as sinkhorn
+from ott.solvers.linear.sinkhorn import Sinkhorn
+from ott.solvers.linear.sinkhorn_lr import LRSinkhorn
+from ott.solvers.quadratic.gromov_wasserstein import GromovWasserstein
+from ott.solvers.quadratic.gromov_wasserstein_lr import LRGromovWasserstein
+
+from moscot._types import ArrayLike, Device_t
+from moscot.backends.ott import GWSolver, SinkhornSolver
+from moscot.backends.ott._utils import alpha_to_fused_penalty
+from moscot.base.output import BaseSolverOutput
+from moscot.base.solver import O, OTSolver
+from moscot.backends.ott._utils import _instantiate_geodesic_cost
+
+import jax.experimental.sparse as jesp
+import scipy.sparse as sp
+import networkx as nx
+from networkx.generators import balanced_tree, random_graphs
+
+
+class TestBackendUtils:
+
+    @staticmethod
+    def test_instantiate_geodesic_cost():
+        m, n = 10, 10
+        problem_shape = 10, 10
+        g = sp.rand(m, n, 0.1, dtype=np.float64)
+        g = jesp.BCOO.from_scipy_sparse(g)
+        geom = _instantiate_geodesic_cost(g, problem_shape, 1.0, False)
+        assert isinstance(geom, Geometry)
+        with pytest.raises(ValueError, match="Expected `x` to have"):
+            _instantiate_geodesic_cost(g, problem_shape, 1.0, True)
+        geom = _instantiate_geodesic_cost(g, (5, 5), 1.0, True)
+
+
+
+
+
+
+