diff --git a/cell2location/models/_cell2location_WTA_module.py b/cell2location/models/_cell2location_WTA_module.py
index 27a5bdd6..d4df08e5 100644
--- a/cell2location/models/_cell2location_WTA_module.py
+++ b/cell2location/models/_cell2location_WTA_module.py
@@ -491,7 +491,7 @@ def forward(self, x_data, neg_data, n_nuclei, idx, batch_index):
         # =====================Compute mRNA count from each factor in locations  ======================= #
         with obs_plate:
             mRNA = w_sf * (self.cell_state * m_g).sum(-1)
-            pyro.deterministic("u_sf_mRNA_factors", mRNA)
+            pyro.deterministic("u_sf_mRNA_factors", mRNA, event_dim=0)
 
     def compute_expected(self, samples, adata_manager, ind_x=None):
         r"""Compute expected expression of each gene in each location. Useful for evaluating how well
diff --git a/cell2location/models/_cell2location_module.py b/cell2location/models/_cell2location_module.py
index 8886d8b0..53290e99 100755
--- a/cell2location/models/_cell2location_module.py
+++ b/cell2location/models/_cell2location_module.py
@@ -480,7 +480,7 @@ def forward(self, x_data, idx, batch_index):
         # =====================Compute mRNA count from each factor in locations  ======================= #
         with obs_plate:
             mRNA = w_sf * (self.cell_state * m_g).sum(-1)
-            pyro.deterministic("u_sf_mRNA_factors", mRNA)
+            pyro.deterministic("u_sf_mRNA_factors", mRNA, event_dim=0)
 
     def compute_expected(
         self,
diff --git a/cell2location/models/simplified/_cell2location_v3_no_factorisation_module.py b/cell2location/models/simplified/_cell2location_v3_no_factorisation_module.py
index 08cd5117..b2817374 100755
--- a/cell2location/models/simplified/_cell2location_v3_no_factorisation_module.py
+++ b/cell2location/models/simplified/_cell2location_v3_no_factorisation_module.py
@@ -355,7 +355,7 @@ def forward(self, x_data, idx, batch_index):
         # =====================Compute mRNA count from each factor in locations  ======================= #
         with obs_plate:
             mRNA = w_sf * (self.cell_state * m_g).sum(-1)
-            pyro.deterministic("u_sf_mRNA_factors", mRNA)
+            pyro.deterministic("u_sf_mRNA_factors", mRNA, event_dim=0)
 
     def compute_expected(self, samples, adata_manager, ind_x=None):
         r"""
diff --git a/cell2location/models/simplified/_cell2location_v3_no_mg_module.py b/cell2location/models/simplified/_cell2location_v3_no_mg_module.py
index 1858c940..48ab6d52 100755
--- a/cell2location/models/simplified/_cell2location_v3_no_mg_module.py
+++ b/cell2location/models/simplified/_cell2location_v3_no_mg_module.py
@@ -344,7 +344,7 @@ def forward(self, x_data, idx, batch_index):
         # =====================Compute mRNA count from each factor in locations  ======================= #
         with obs_plate:
             mRNA = w_sf * (self.cell_state).sum(-1)
-            pyro.deterministic("u_sf_mRNA_factors", mRNA)
+            pyro.deterministic("u_sf_mRNA_factors", mRNA, event_dim=0)
 
     def compute_expected(self, samples, adata_manager, ind_x=None):
         r"""Compute expected expression of each gene in each location. Useful for evaluating how well
diff --git a/tests/test_deterministic_sites.py b/tests/test_deterministic_sites.py
new file mode 100644
index 00000000..9567e6d0
--- /dev/null
+++ b/tests/test_deterministic_sites.py
@@ -0,0 +1,94 @@
+import anndata as ad
+import numpy as np
+import pandas as pd
+import pyro
+import pytest
+from scipy import sparse
+from scvi.dataloaders import AnnDataLoader
+
+from cell2location.models import Cell2location, Cell2location_WTA
+from cell2location.models._cell2location_module import (
+    LocationModelLinearDependentWMultiExperimentLocationBackgroundNormLevelGeneAlphaPyroModel,
+)
+from cell2location.models.simplified._cell2location_v3_no_factorisation_module import (
+    LocationModelMultiExperimentLocationBackgroundNormLevelGeneAlphaPyroModel,
+)
+from cell2location.models.simplified._cell2location_v3_no_mg_module import (
+    LocationModelLinearDependentWMultiExperimentLocationBackgroundNormLevelNoMGPyroModel,
+)
+
+SITE_NAME = "u_sf_mRNA_factors"
+
+
+def make_random_problem(n_obs=8, n_genes=16, n_factors=3, seed=0):
+    rng = np.random.default_rng(seed)
+    genes = pd.Index([f"gene_{i}" for i in range(n_genes)])
+    factors = [f"cell_type_{i}" for i in range(n_factors)]
+    signatures = rng.gamma(2.0, 1.0, size=(n_genes, n_factors)).astype(np.float32)
+    counts = rng.poisson(2.0, size=(n_obs, n_genes)).astype(np.float32)
+    adata = ad.AnnData(
+        X=sparse.csr_matrix(counts),
+        obs=pd.DataFrame(index=[f"location_{i}" for i in range(n_obs)]),
+        var=pd.DataFrame(index=genes),
+    )
+    return adata, pd.DataFrame(signatures, index=genes, columns=factors)
+
+
+def unwrap_base_distribution(distribution):
+    while hasattr(distribution, "base_dist"):
+        distribution = distribution.base_dist
+    return distribution
+
+
+@pytest.mark.parametrize(
+    "model_class",
+    [
+        LocationModelLinearDependentWMultiExperimentLocationBackgroundNormLevelGeneAlphaPyroModel,
+        LocationModelMultiExperimentLocationBackgroundNormLevelGeneAlphaPyroModel,
+        LocationModelLinearDependentWMultiExperimentLocationBackgroundNormLevelNoMGPyroModel,
+    ],
+)
+def test_mrna_factors_delta_has_linear_shape(model_class):
+    n_obs, n_factors = 8, 3
+    adata, cell_state_df = make_random_problem(n_obs=n_obs, n_factors=n_factors)
+    Cell2location.setup_anndata(adata)
+    model = Cell2location(
+        adata,
+        cell_state_df=cell_state_df,
+        model_class=model_class,
+        N_cells_per_location=3,
+        detection_alpha=20,
+    )
+    loader = AnnDataLoader(model.adata_manager, shuffle=False, batch_size=n_obs)
+    model_args, model_kwargs = model.module._get_fn_args_from_batch(next(iter(loader)))
+
+    trace = pyro.poutine.trace(model.module.model).get_trace(*model_args, **model_kwargs)
+    node = trace.nodes[SITE_NAME]
+    delta = unwrap_base_distribution(node["fn"])
+
+    assert tuple(node["value"].shape) == (n_obs, n_factors)
+    assert tuple(delta.v.shape) == (n_obs, n_factors)
+    assert delta.v.numel() == n_obs * n_factors
+
+
+def test_wta_mrna_factors_delta_has_linear_shape():
+    n_obs, n_factors = 8, 3
+    adata, cell_state_df = make_random_problem(n_obs=n_obs, n_factors=n_factors)
+    adata.obs["nuclei"] = 3.0
+    adata.obsm["negative_probes"] = np.ones((n_obs, 2), dtype=np.float32)
+    Cell2location_WTA.setup_anndata(adata, nuclei_key="nuclei", neg_probes_key="negative_probes")
+    model = Cell2location_WTA(
+        adata,
+        cell_state_df=cell_state_df,
+        detection_alpha=20,
+    )
+    loader = AnnDataLoader(model.adata_manager, shuffle=False, batch_size=n_obs)
+    model_args, model_kwargs = model.module._get_fn_args_from_batch(next(iter(loader)))
+
+    trace = pyro.poutine.trace(model.module.model).get_trace(*model_args, **model_kwargs)
+    node = trace.nodes[SITE_NAME]
+    delta = unwrap_base_distribution(node["fn"])
+
+    assert tuple(node["value"].shape) == (n_obs, n_factors)
+    assert tuple(delta.v.shape) == (n_obs, n_factors)
+    assert delta.v.numel() == n_obs * n_factors