diff --git a/botorch/test_functions/base.py b/botorch/test_functions/base.py
index 3c05d4fef7..b0dbf37f76 100644
--- a/botorch/test_functions/base.py
+++ b/botorch/test_functions/base.py
@@ -55,26 +55,33 @@ def forward(self, X: Tensor, noise: bool = True) -> Tensor:
         r"""Evaluate the function on a set of points.
 
         Args:
-            X: A `batch_shape x d`-dim tensor of point(s) at which to evaluate the
-                function.
+            X: A `(batch_shape) x d`-dim tensor of point(s) at which to evaluate
+                the function.
             noise: If `True`, add observation noise as specified by `noise_std`.
 
         Returns:
             A `batch_shape`-dim tensor ouf function evaluations.
         """
-        batch = X.ndimension() > 1
-        X = X if batch else X.unsqueeze(0)
         f = self.evaluate_true(X=X)
         if noise and self.noise_std is not None:
             _noise = torch.tensor(self.noise_std, device=X.device, dtype=X.dtype)
             f += _noise * torch.randn_like(f)
         if self.negate:
             f = -f
-        return f if batch else f.squeeze(0)
+        return f
 
     @abstractmethod
     def evaluate_true(self, X: Tensor) -> Tensor:
-        r"""Evaluate the function (w/o observation noise) on a set of points."""
+        r"""
+        Evaluate the function (w/o observation noise) on a set of points.
+
+        Args:
+            X: A `(batch_shape) x d`-dim tensor of point(s) at which to
+                evaluate.
+
+        Returns:
+            A `batch_shape`-dim tensor.
+        """
         pass  # pragma: no cover
 
 
diff --git a/botorch/test_functions/multi_fidelity.py b/botorch/test_functions/multi_fidelity.py
index d072664a8c..dd2d057f0b 100644
--- a/botorch/test_functions/multi_fidelity.py
+++ b/botorch/test_functions/multi_fidelity.py
@@ -46,7 +46,7 @@ class AugmentedBranin(SyntheticTestFunction):
     def evaluate_true(self, X: Tensor) -> Tensor:
         t1 = (
             X[..., 1]
-            - (5.1 / (4 * math.pi**2) - 0.1 * (1 - X[:, 2])) * X[:, 0].pow(2)
+            - (5.1 / (4 * math.pi**2) - 0.1 * (1 - X[..., 2])) * X[..., 0].pow(2)
             + 5 / math.pi * X[..., 0]
             - 6
         )
diff --git a/botorch/utils/testing.py b/botorch/utils/testing.py
index bcb41462b6..e0cfc6d035 100644
--- a/botorch/utils/testing.py
+++ b/botorch/utils/testing.py
@@ -11,6 +11,7 @@
 from abc import abstractproperty
 from collections import OrderedDict
 from collections.abc import Sequence
+from itertools import product
 from typing import Any, Optional
 from unittest import mock, TestCase
 
@@ -102,15 +103,22 @@ def assertAllClose(
 
 
 class BaseTestProblemTestCaseMixIn:
-    def test_forward(self):
-        for dtype in (torch.float, torch.double):
-            for batch_shape in (torch.Size(), torch.Size([2]), torch.Size([2, 3])):
-                for f in self.functions:
-                    f.to(device=self.device, dtype=dtype)
-                    X = torch.rand(*batch_shape, f.dim, device=self.device, dtype=dtype)
-                    X = f.bounds[0] + X * (f.bounds[1] - f.bounds[0])
-                    res = f(X)
-                    f(X, noise=False)
+    def test_forward_and_evaluate_true(self):
+        dtypes = (torch.float, torch.double)
+        batch_shapes = (torch.Size(), torch.Size([2]), torch.Size([2, 3]))
+        for dtype, batch_shape, f in product(dtypes, batch_shapes, self.functions):
+            f.to(device=self.device, dtype=dtype)
+            X = torch.rand(*batch_shape, f.dim, device=self.device, dtype=dtype)
+            X = f.bounds[0] + X * (f.bounds[1] - f.bounds[0])
+            res_forward = f(X)
+            res_evaluate_true = f.evaluate_true(X)
+            for method, res in {
+                "forward": res_forward,
+                "evaluate_true": res_evaluate_true,
+            }.items():
+                with self.subTest(
+                    f"{dtype}_{batch_shape}_{f.__class__.__name__}_{method}"
+                ):
                     self.assertEqual(res.dtype, dtype)
                     self.assertEqual(res.device.type, self.device.type)
                     tail_shape = torch.Size(
@@ -340,7 +348,7 @@ def posterior(
         X: Tensor,
         output_indices: Optional[list[int]] = None,
         posterior_transform: Optional[PosteriorTransform] = None,
-        observation_noise: bool = False,
+        observation_noise: bool | torch.Tensor = False,
     ) -> MockPosterior:
         if posterior_transform is not None:
             return posterior_transform(self._posterior)
@@ -357,7 +365,7 @@ def batch_shape(self) -> torch.Size:
         extended_shape = self._posterior._extended_shape()
         return extended_shape[:-2]
 
-    def state_dict(self) -> None:
+    def state_dict(self, *args, **kwargs) -> None:
         pass
 
     def load_state_dict(