diff --git a/src/moscot/datasets.py b/src/moscot/datasets.py
index 7728d66cc..a308d5867 100644
--- a/src/moscot/datasets.py
+++ b/src/moscot/datasets.py
@@ -5,12 +5,14 @@
 import shutil
 import tempfile
 import urllib.request
+from itertools import combinations
 from types import MappingProxyType
 from typing import Any, Dict, List, Literal, Mapping, Optional, Tuple
 
 import networkx as nx
 import numpy as np
 import pandas as pd
+from scipy.linalg import block_diag
 
 import anndata as ad
 from anndata import AnnData
@@ -411,7 +413,8 @@ def simulate_data(
         Literal indicating whether to add costs corresponding to a specific problem setting.
         If `None`, no quadratic cost element is generated.
     lin_cost_matrix
-        Key where to save the linear cost matrix. If `None`, no linear cost matrix is generated.
+        Key where to save the linear cost matrix. It is generated according to the pairwise policy.
+        If `None`, no linear cost matrix is generated.
     quad_cost_matrix
         Key where to save the quadratic cost matrices. If `None`, no quadratic cost matrix is generated.
 
@@ -457,9 +460,18 @@ def simulate_data(
         barcode_dim = kwargs.pop("barcode_dim", 10)
         adata.obsm["barcode"] = rng.choice(n_intBCs, size=(adata.n_obs, barcode_dim))
     if lin_cost_matrix is not None:
-        raise NotImplementedError("TODO")
+        adata.uns[lin_cost_matrix] = {}
+        for i, j in combinations(range(n_distributions), 2):
+            adata.uns[lin_cost_matrix][(str(i), str(j))] = np.abs(
+                rng.normal(size=(cells_per_distribution, cells_per_distribution))
+            )
     if quad_cost_matrix is not None:
-        raise NotImplementedError("TODO")
+        quad_costs = [
+            (np.abs(rng.normal(size=(cells_per_distribution, cells_per_distribution)))) for i in range(n_distributions)
+        ]
+        quad_cm = block_diag(*quad_costs)
+        np.fill_diagonal(quad_cm, 0)
+        adata.obsp[quad_cost_matrix] = quad_cm
     return adata