diff --git a/botorch/models/transforms/input.py b/botorch/models/transforms/input.py
index 0efb263191..22a70d8f87 100644
--- a/botorch/models/transforms/input.py
+++ b/botorch/models/transforms/input.py
@@ -614,7 +614,7 @@ def _update_coefficients(self, X: Tensor) -> None:
 
 
 class Normalize(AffineInputTransform):
-    r"""Normalize the inputs to the unit cube.
+    r"""Normalize the inputs have unit range and be centered at 0.5 (by default).
 
     If no explicit bounds are provided this module is stateful: If in train mode,
     calling `forward` updates the module state (i.e. the normalizing bounds). If
@@ -635,6 +635,7 @@ def __init__(
         min_range: float = 1e-8,
         learn_bounds: bool | None = None,
         almost_zero: float = 1e-12,
+        center: float = 0.5,
     ) -> None:
         r"""Normalize the inputs to the unit cube.
 
@@ -662,6 +663,7 @@ def __init__(
                 NOTE: This only applies if `learn_bounds=True`.
             learn_bounds: Whether to learn the bounds in train mode. Defaults
                 to False if bounds are provided, otherwise defaults to True.
+            center: The center of the range for each parameter. Default: 0.5.
 
         Example:
             >>> t = Normalize(d=2)
@@ -704,10 +706,11 @@ def __init__(
                     "will not be updated and the transform will be a no-op.",
                     UserInputWarning,
                 )
+        self.center = center
         super().__init__(
             d=d,
             coefficient=coefficient,
-            offset=offset,
+            offset=offset + (0.5 - center) * coefficient,
             indices=indices,
             batch_shape=batch_shape,
             transform_on_train=transform_on_train,
@@ -745,7 +748,10 @@ def _update_coefficients(self, X) -> None:
         coefficient = torch.amax(X, dim=reduce_dims).unsqueeze(-2) - offset
         almost_zero = coefficient < self.min_range
         self._coefficient = torch.where(almost_zero, 1.0, coefficient)
-        self._offset = torch.where(almost_zero, 0.0, offset)
+        self._offset = (
+            torch.where(almost_zero, 0.0, offset)
+            + (0.5 - self.center) * self._coefficient
+        )
 
     def get_init_args(self) -> dict[str, Any]:
         r"""Get the arguments necessary to construct an exact copy of the transform."""
diff --git a/test/models/transforms/test_input.py b/test/models/transforms/test_input.py
index b2945f30fc..267046389c 100644
--- a/test/models/transforms/test_input.py
+++ b/test/models/transforms/test_input.py
@@ -7,6 +7,7 @@
 import itertools
 from abc import ABC
 from copy import deepcopy
+from itertools import product
 from random import randint
 
 import torch
@@ -259,17 +260,19 @@ def test_normalize(self) -> None:
                 nlz(X)
 
             # basic usage
-            for batch_shape in (torch.Size(), torch.Size([3])):
+            for batch_shape, center in product(
+                (torch.Size(), torch.Size([3])), [0.5, 0.0]
+            ):
                 # learned bounds
-                nlz = Normalize(d=2, batch_shape=batch_shape)
+                nlz = Normalize(d=2, batch_shape=batch_shape, center=center)
                 X = torch.randn(*batch_shape, 4, 2, device=self.device, dtype=dtype)
                 for _X in (torch.stack((X, X)), X):  # check batch_shape is obeyed
                     X_nlzd = nlz(_X)
                     self.assertEqual(nlz.mins.shape, batch_shape + (1, X.shape[-1]))
                     self.assertEqual(nlz.ranges.shape, batch_shape + (1, X.shape[-1]))
 
-                self.assertEqual(X_nlzd.min().item(), 0.0)
-                self.assertEqual(X_nlzd.max().item(), 1.0)
+                self.assertAllClose(X_nlzd.min().item(), center - 0.5)
+                self.assertAllClose(X_nlzd.max().item(), center + 0.5)
 
                 nlz.eval()
                 X_unnlzd = nlz.untransform(X_nlzd)
@@ -278,6 +281,9 @@ def test_normalize(self) -> None:
                     [X.min(dim=-2, keepdim=True)[0], X.max(dim=-2, keepdim=True)[0]],
                     dim=-2,
                 )
+                coeff = expected_bounds[..., 1, :] - expected_bounds[..., 0, :]
+                expected_bounds[..., 0, :] += (0.5 - center) * coeff
+                expected_bounds[..., 1, :] = expected_bounds[..., 0, :] + coeff
                 atol = 1e-6 if dtype is torch.float32 else 1e-12
                 rtol = 1e-4 if dtype is torch.float32 else 1e-8
                 self.assertAllClose(nlz.bounds, expected_bounds, atol=atol, rtol=rtol)