diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6be4b063f..4171691f8 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,6 +1,7 @@
 # v0.14.3
 
 - Fixup for conditional correlation matrix (thanks @JBeckUniTb, #404)
+- z-score data using only the training data (#411)
 
 
 # v0.14.2
diff --git a/sbi/inference/snle/snle_base.py b/sbi/inference/snle/snle_base.py
index 2ba653d16..da9844742 100644
--- a/sbi/inference/snle/snle_base.py
+++ b/sbi/inference/snle/snle_base.py
@@ -148,18 +148,6 @@ def train(
         self._round = max(self._data_round_index)
         theta, x, _ = self.get_simulations(self._round, exclude_invalid_x, False)
 
-        # First round or if retraining from scratch:
-        # Call the `self._build_neural_net` with the rounds' thetas and xs as
-        # arguments, which will build the neural network
-        # This is passed into NeuralPosterior, to create a neural posterior which
-        # can `sample()` and `log_prob()`. The network is accessible via `.net`.
-        if self._neural_net is None or retrain_from_scratch_each_round:
-            self._neural_net = self._build_neural_net(theta, x)
-            self._x_shape = x_shape_from_simulation(x)
-            assert (
-                len(self._x_shape) < 3
-            ), "SNLE cannot handle multi-dimensional simulator output."
-
         # Starting index for the training set (1 = discard round-0 samples).
         start_idx = int(discard_prior_samples and self._round > 0)
         theta, x, _ = self.get_simulations(start_idx, exclude_invalid_x)
@@ -194,6 +182,20 @@ def train(
             sampler=SubsetRandomSampler(val_indices),
         )
 
+        # First round or if retraining from scratch:
+        # Call the `self._build_neural_net` with the rounds' thetas and xs as
+        # arguments, which will build the neural network
+        # This is passed into NeuralPosterior, to create a neural posterior which
+        # can `sample()` and `log_prob()`. The network is accessible via `.net`.
+        if self._neural_net is None or retrain_from_scratch_each_round:
+            self._neural_net = self._build_neural_net(
+                theta[train_indices], x[train_indices]
+            )
+            self._x_shape = x_shape_from_simulation(x)
+            assert (
+                len(self._x_shape) < 3
+            ), "SNLE cannot handle multi-dimensional simulator output."
+
         self._neural_net.to(self._device)
         optimizer = optim.Adam(list(self._neural_net.parameters()), lr=learning_rate,)
 
diff --git a/sbi/inference/snpe/snpe_base.py b/sbi/inference/snpe/snpe_base.py
index fdc900879..0b3fd03b3 100644
--- a/sbi/inference/snpe/snpe_base.py
+++ b/sbi/inference/snpe/snpe_base.py
@@ -189,16 +189,6 @@ def train(
         # Load data from most recent round.
         theta, x, _ = self.get_simulations(self._round, exclude_invalid_x, False)
 
-        # First round or if retraining from scratch:
-        # Call the `self._build_neural_net` with the rounds' thetas and xs as
-        # arguments, which will build the neural network.
-        # This is passed into NeuralPosterior, to create a neural posterior which
-        # can `sample()` and `log_prob()`. The network is accessible via `.net`.
-        if self._neural_net is None or retrain_from_scratch_each_round:
-            self._neural_net = self._build_neural_net(theta, x)
-            test_posterior_net_for_multi_d_x(self._neural_net, theta, x)
-            self._x_shape = x_shape_from_simulation(x)
-
         # Starting index for the training set (1 = discard round-0 samples).
         start_idx = int(discard_prior_samples and self._round > 0)
 
@@ -242,6 +232,18 @@ def train(
             sampler=SubsetRandomSampler(val_indices),
         )
 
+        # First round or if retraining from scratch:
+        # Call the `self._build_neural_net` with the rounds' thetas and xs as
+        # arguments, which will build the neural network.
+        # This is passed into NeuralPosterior, to create a neural posterior which
+        # can `sample()` and `log_prob()`. The network is accessible via `.net`.
+        if self._neural_net is None or retrain_from_scratch_each_round:
+            self._neural_net = self._build_neural_net(
+                theta[train_indices], x[train_indices]
+            )
+            test_posterior_net_for_multi_d_x(self._neural_net, theta, x)
+            self._x_shape = x_shape_from_simulation(x)
+
         # Move entire net to device for training.
         self._neural_net.to(self._device)
         optimizer = optim.Adam(list(self._neural_net.parameters()), lr=learning_rate,)
diff --git a/sbi/inference/snre/snre_base.py b/sbi/inference/snre/snre_base.py
index 071531f74..488ccd6e9 100644
--- a/sbi/inference/snre/snre_base.py
+++ b/sbi/inference/snre/snre_base.py
@@ -150,19 +150,6 @@ def train(
         self._round = max(self._data_round_index)
         theta, x, _ = self.get_simulations(self._round, exclude_invalid_x, False)
 
-        # First round or if retraining from scratch:
-        # Call the `self._build_neural_net` with the rounds' thetas and xs as
-        # arguments, which will build the neural network
-        # This is passed into NeuralPosterior, to create a neural posterior which
-        # can `sample()` and `log_prob()`. The network is accessible via `.net`.
-        if self._neural_net is None or retrain_from_scratch_each_round:
-            self._neural_net = self._build_neural_net(theta, x)
-            self._x_shape = x_shape_from_simulation(x)
-            assert len(self._x_shape) < 3, (
-                "For now, SNRE cannot handle multi-dimensional simulator output, see "
-                "issue #360."
-            )
-
         # Starting index for the training set (1 = discard round-0 samples).
         start_idx = int(discard_prior_samples and self._round > 0)
         theta, x, _ = self.get_simulations(start_idx, exclude_invalid_x)
@@ -203,6 +190,21 @@ def train(
             sampler=SubsetRandomSampler(val_indices),
         )
 
+        # First round or if retraining from scratch:
+        # Call the `self._build_neural_net` with the rounds' thetas and xs as
+        # arguments, which will build the neural network
+        # This is passed into NeuralPosterior, to create a neural posterior which
+        # can `sample()` and `log_prob()`. The network is accessible via `.net`.
+        if self._neural_net is None or retrain_from_scratch_each_round:
+            self._neural_net = self._build_neural_net(
+                theta[train_indices], x[train_indices]
+            )
+            self._x_shape = x_shape_from_simulation(x)
+            assert len(self._x_shape) < 3, (
+                "For now, SNRE cannot handle multi-dimensional simulator output, see "
+                "issue #360."
+            )
+
         self._neural_net.to(self._device)
         optimizer = optim.Adam(list(self._neural_net.parameters()), lr=learning_rate,)
 
diff --git a/tests/inference_with_NaN_simulator_test.py b/tests/inference_with_NaN_simulator_test.py
index ec03d6dd2..6ddba1fd4 100644
--- a/tests/inference_with_NaN_simulator_test.py
+++ b/tests/inference_with_NaN_simulator_test.py
@@ -121,7 +121,7 @@ def linear_gaussian_nan(
     num_rounds = 2
 
     for r in range(num_rounds):
-        theta, x = simulate_for_sbi(simulator, proposals[-1], 500)
+        theta, x = simulate_for_sbi(simulator, proposals[-1], 550)
         rejection_estimator.append_simulations(theta, x)
         if r < num_rounds - 1:
             _ = rejection_estimator.train()