diff --git a/docs/tutorials/neural/200_Monge_Gap.ipynb b/docs/tutorials/neural/200_Monge_Gap.ipynb
index 5dac8c025..bb88c1725 100644
--- a/docs/tutorials/neural/200_Monge_Gap.ipynb
+++ b/docs/tutorials/neural/200_Monge_Gap.ipynb
@@ -50,7 +50,7 @@
     "\n",
     "The first requirement (efficiency) can be quantified with the **Monge gap** $\\mathcal{M}_\\mu^c$, a non-negative regularizer defined through $\\mu$ and $c$, and which takes as an argument any map $T : \\mathbb{R}^d \\rightarrow \\mathbb{R}^d$. The value $\\mathcal{M}_\\mu^c(T)$ quantifies how $T$ moves mass efficiently between $\\mu$ and $T \\sharp \\mu$, and only cancels $\\mathcal{M}_\\mu^c(T) = 0$ i.f.f. $T$ is optimal between $\\mu$ and $T \\sharp \\mu$ for the cost $c$.\n",
     "\n",
-    "The second requirement (landing on $\\nu$) is then simply handled using a fitting loss $\\Delta$ between $T \\sharp \\mu$ and $\\nu$. This can be measured, e.g., using a {func}`~ott.tools.sinkhorn_divergence.sinkhorn_divergence`. Introducing a regularization strength $\\lambda_\\mathrm{MG} > 0$, looking for a Monge map can be reformulated as finding a $T$ that minimizes:\n",
+    "The second requirement (landing on $\\nu$) is then simply handled using a fitting loss $\\Delta$ between $T \\sharp \\mu$ and $\\nu$. This can be measured, e.g., using the Sinkhorn divergence, {func}`~ott.tools.sinkhorn_divergence.sinkdiv`. Introducing a regularization strength $\\lambda_\\mathrm{MG} > 0$, looking for a Monge map can be reformulated as finding a $T$ that minimizes:\n",
     "\n",
     "$$\n",
     "\\min_{T:\\mathbb{R}^d \\rightarrow \\mathbb{R}^d} \\Delta(T\\sharp \\mu, \\nu) + \\lambda_\\mathrm{MG} \\mathcal{M}_\\mu^c(T)\n",
@@ -324,8 +324,7 @@
     "$$\n",
     "\\min_{T:\\mathbb{R}^d \\rightarrow \\mathbb{R}^d} \\Delta(T\\sharp \\mu, \\nu) + \\lambda_\\mathrm{MG} \\mathcal{M}_\\mu^c(T)\n",
     "$$\n",
-    "For all fittings, we use $\\Delta = S_{\\varepsilon, \\ell_2^2}$, the {func}`~ott.tools.sinkhorn_divergence.sinkhorn_divergence` with the {class}`squared Euclidean cost <ott.geometry.costs.SqEuclidean>`\n",
-    "The function considers a ground cost function `cost_fn` (corresponding to $c$), as well as the `epsilon` regularization parameters to compute approximated Wasserstein distances, both for fitting and regularizer."
+    "For all fittings, we use $\\Delta = S_{\\varepsilon, \\ell_2^2}$, the :term:`Sinkhorn divergence`, {func}`~ott.tools.sinkhorn_divergence.sinkdiv` with the {class}`squared Euclidean cost <ott.geometry.costs.SqEuclidean>` :term:`ground cost` function `cost_fn` (corresponding to $c$), as well as the `epsilon` regularization parameters to compute approximated Wasserstein distances, both for fitting and regularizer."
    ]
   },
   {
@@ -359,8 +358,8 @@
     "\n",
     "    @jax.jit\n",
     "    def fitting_loss(x, y):\n",
-    "        div, out = sinkhorn_divergence.sinkhorn_divergence(\n",
-    "            pointcloud.PointCloud, x, y, epsilon=epsilon_fitting, static_b=True\n",
+    "        div, out = sinkhorn_divergence.sinkdiv(\n",
+    "            x, y, epsilon=epsilon_fitting, static_b=True\n",
     "        )\n",
     "        return div, out.n_iters\n",
     "\n",
diff --git a/src/ott/neural/methods/monge_gap.py b/src/ott/neural/methods/monge_gap.py
index 71e3446fb..6dbf7c0d9 100644
--- a/src/ott/neural/methods/monge_gap.py
+++ b/src/ott/neural/methods/monge_gap.py
@@ -184,7 +184,7 @@ class MongeGapEstimator:
   sets of points.
 
   For instance, :math:`\Delta` can be the
-  :func:`~ott.tools.sinkhorn_divergence.sinkhorn_divergence`
+  :func:`~ott.tools.sinkhorn_divergence.sinkdiv`
   and :math:`R` the :func:`~ott.neural.methods.monge_gap.monge_gap_from_samples`
   :cite:`uscidda:23` for a given cost function :math:`c`.
   In that case, it estimates a :math:`c`-OT map, i.e. a map :math:`T`
@@ -260,7 +260,8 @@ def setup(
   def regularizer(self) -> Callable[[jnp.ndarray, jnp.ndarray], float]:
     """Regularizer added to the fitting loss.
 
-    Can be, e.g. the :func:`~ott.neural.methods.monge_gap.monge_gap_from_samples`.
+    Can be, e.g. the
+    :func:`~ott.neural.methods.monge_gap.monge_gap_from_samples`.
     If no regularizer is passed for solver instantiation,
     or regularization weight :attr:`regularizer_strength` is 0,
     return 0 by default along with an empty set of log values.
@@ -273,7 +274,7 @@ def regularizer(self) -> Callable[[jnp.ndarray, jnp.ndarray], float]:
   def fitting_loss(self) -> Callable[[jnp.ndarray, jnp.ndarray], float]:
     """Fitting loss to fit the marginal constraint.
 
-    Can be, e.g. :func:`~ott.tools.sinkhorn_divergence.sinkhorn_divergence`.
+    Can be, e.g. :func:`~ott.tools.sinkhorn_divergence.sinkdiv`.
     If no fitting_loss is passed for solver instantiation, return 0 by default,
     and no log values.
     """
diff --git a/tests/neural/methods/monge_gap_test.py b/tests/neural/methods/monge_gap_test.py
index 8a546d890..397bcaa19 100644
--- a/tests/neural/methods/monge_gap_test.py
+++ b/tests/neural/methods/monge_gap_test.py
@@ -20,7 +20,7 @@
 import numpy as np
 
 from ott import datasets
-from ott.geometry import costs, pointcloud, regularizers
+from ott.geometry import costs, regularizers
 from ott.neural.methods import monge_gap
 from ott.neural.networks import potentials
 from ott.tools import sinkhorn_divergence
@@ -144,8 +144,7 @@ def fitting_loss(
         mapped_samples: jnp.ndarray,
     ) -> Optional[float]:
       r"""Sinkhorn divergence fitting loss."""
-      div, _ = sinkhorn_divergence.sinkhorn_divergence(
-          pointcloud.PointCloud,
+      div, _ = sinkhorn_divergence.sinkdiv(
           x=samples,
           y=mapped_samples,
       )