diff --git a/monai/transforms/intensity/array.py b/monai/transforms/intensity/array.py
index a23c867d60a..3612d5559d1 100644
--- a/monai/transforms/intensity/array.py
+++ b/monai/transforms/intensity/array.py
@@ -2614,7 +2614,7 @@ def __call__(self, img: torch.Tensor) -> torch.Tensor:
         grid = torch.arange(len(noise)) / len(noise)
         noise += self.slope * grid
         # rescale
-        noise = (noise - noise.min()) / (noise.max() - noise.min()) * img_.max() + img_.min()
+        noise = (noise - noise.min()) / (noise.max() - noise.min()) * (img_.max() - img_.min()) + img_.min()
 
         # intensity remapping function
         index_img = torch.bucketize(img_, torch.tensor(vals_to_sample))
@@ -2661,17 +2661,18 @@ def __call__(self, img: torch.Tensor) -> torch.Tensor:
         img = convert_to_tensor(img, track_meta=get_track_meta())
         if self._do_transform:
             if self.channel_wise:
-                img = torch.stack(
-                    [
-                        IntensityRemap(self.kernel_size, self.R.choice([-self.slope, self.slope]))(img[i])
-                        for i in range(len(img))
-                    ]
-                )
+                img = torch.stack([self._remap(img[i]) for i in range(len(img))])
             else:
-                img = IntensityRemap(self.kernel_size, self.R.choice([-self.slope, self.slope]))(img)
+                img = self._remap(img)
 
         return img
 
+    def _remap(self, img: torch.Tensor) -> torch.Tensor:
+        # share this transform's random state so that `set_random_state` also controls the remapping curve
+        remap = IntensityRemap(self.kernel_size, self.R.choice([-self.slope, self.slope]))
+        remap.set_random_state(state=self.R)
+        return remap(img)
+
 
 class ForegroundMask(Transform):
     """
diff --git a/tests/transforms/test_intensity_remap.py b/tests/transforms/test_intensity_remap.py
new file mode 100644
index 00000000000..6c1f8620062
--- /dev/null
+++ b/tests/transforms/test_intensity_remap.py
@@ -0,0 +1,67 @@
+# Copyright (c) MONAI Consortium
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#     http://www.apache.org/licenses/LICENSE-2.0
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import annotations
+
+import unittest
+
+import torch
+from parameterized import parameterized
+
+from monai.transforms import IntensityRemap, RandIntensityRemap
+from tests.test_utils import assert_allclose
+
+# input ranges with a negative, zero and positive minimum
+TEST_RANGES = [(-1000.0, 3000.0), (0.0, 255.0), (10.0, 20.0)]
+
+
+class TestIntensityRemap(unittest.TestCase):
+    @parameterized.expand(TEST_RANGES)
+    def test_output_range(self, low, high):
+        img = torch.linspace(low, high, 500).reshape(1, 10, 50)
+        remap = IntensityRemap(kernel_size=10, slope=0.7)
+        remap.set_random_state(seed=0)
+        result = remap(img)
+        self.assertEqual(result.shape, img.shape)
+        assert_allclose(result.min(), low, type_test=False, atol=1e-3, rtol=1e-5)
+        assert_allclose(result.max(), high, type_test=False, atol=1e-3, rtol=1e-5)
+
+
+class TestRandIntensityRemap(unittest.TestCase):
+    @parameterized.expand(TEST_RANGES)
+    def test_output_range(self, low, high):
+        img = torch.stack([torch.linspace(low, high, 500).reshape(10, 50)] * 2)
+        remap = RandIntensityRemap(prob=1.0, kernel_size=10, channel_wise=True)
+        remap.set_random_state(seed=0)
+        result = remap(img)
+        self.assertEqual(result.shape, img.shape)
+        for c in range(img.shape[0]):
+            assert_allclose(result[c].min(), low, type_test=False, atol=1e-3, rtol=1e-5)
+            assert_allclose(result[c].max(), high, type_test=False, atol=1e-3, rtol=1e-5)
+
+    @parameterized.expand([[True], [False]])
+    def test_set_random_state(self, channel_wise):
+        img = torch.stack([torch.linspace(0.0, 100.0, 500).reshape(10, 50)] * 2)
+        results = []
+        for _ in range(2):
+            remap = RandIntensityRemap(prob=1.0, kernel_size=10, channel_wise=channel_wise)
+            remap.set_random_state(seed=0)
+            results.append(remap(img))
+        assert_allclose(results[0], results[1], type_test=False)
+
+    def test_prob_zero(self):
+        img = torch.linspace(-1.0, 1.0, 500).reshape(1, 10, 50)
+        remap = RandIntensityRemap(prob=0.0)
+        assert_allclose(remap(img), img, type_test=False)
+
+
+if __name__ == "__main__":
+    unittest.main()