diff --git a/src/pyrecest/filters/interacting_multiple_model_filter.py b/src/pyrecest/filters/interacting_multiple_model_filter.py
index 4ed276933b..0e81c4fb53 100644
--- a/src/pyrecest/filters/interacting_multiple_model_filter.py
+++ b/src/pyrecest/filters/interacting_multiple_model_filter.py
@@ -471,17 +471,22 @@ def _prepare_transition_matrix(transition_matrix, n_models):
         if pyrecest.backend.any(transition_matrix < 0.0):
             raise ValueError("transition_matrix must be elementwise nonnegative.")
 
-        row_sums = transition_matrix.sum(axis=1)
-        if pyrecest.backend.any(row_sums <= 0.0):
+        row_scales = pyrecest.backend.max(transition_matrix, axis=1)
+        if pyrecest.backend.any(row_scales <= 0.0):
             raise ValueError(
                 "Each row of transition_matrix must sum to a positive value."
             )
-        if not allclose(row_sums, 1.0):
+
+        rows_are_normalized = bool(
+            pyrecest.backend.all(transition_matrix <= 1.0)
+        ) and allclose(transition_matrix.sum(axis=1), 1.0)
+        if not rows_are_normalized:
             warnings.warn(
                 "Rows of transition_matrix do not sum to one. Renormalizing rows.",
                 UserWarning,
             )
-            transition_matrix = transition_matrix / row_sums[:, None]
+            scaled_rows = transition_matrix / row_scales[:, None]
+            transition_matrix = scaled_rows / scaled_rows.sum(axis=1)[:, None]
         return transition_matrix
 
     @staticmethod
diff --git a/tests/filters/test_imm_transition_matrix_overflow.py b/tests/filters/test_imm_transition_matrix_overflow.py
new file mode 100644
index 0000000000..79ed5c798e
--- /dev/null
+++ b/tests/filters/test_imm_transition_matrix_overflow.py
@@ -0,0 +1,42 @@
+import unittest
+
+import numpy as np
+import numpy.testing as npt
+
+from pyrecest.filters.interacting_multiple_model_filter import (
+    InteractingMultipleModelFilter,
+)
+
+
+class TestIMMTransitionMatrixOverflow(unittest.TestCase):
+    def test_normalizes_finite_rows_without_overflow(self):
+        max_float = np.finfo(float).max
+        transition_matrix = np.array(
+            [
+                [max_float, max_float / 2.0],
+                [1.0, 1.0],
+            ]
+        )
+
+        with np.errstate(over="raise", invalid="raise", divide="raise"):
+            with self.assertWarnsRegex(UserWarning, "Renormalizing rows"):
+                normalized = (
+                    InteractingMultipleModelFilter._prepare_transition_matrix(
+                        transition_matrix, 2
+                    )
+                )
+
+        npt.assert_allclose(
+            normalized,
+            np.array(
+                [
+                    [2.0 / 3.0, 1.0 / 3.0],
+                    [0.5, 0.5],
+                ]
+            ),
+        )
+        npt.assert_allclose(normalized.sum(axis=1), np.ones(2))
+
+
+if __name__ == "__main__":
+    unittest.main()