diff --git a/pytensor/assumptions/diagonal.py b/pytensor/assumptions/diagonal.py
index 36f160e287..ae8b4ded19 100644
--- a/pytensor/assumptions/diagonal.py
+++ b/pytensor/assumptions/diagonal.py
@@ -49,8 +49,13 @@ def _diagonal_from_constant(var: TensorConstant) -> FactState:
         if m != n:
             result = FactState.FALSE
         else:
-            eye_mask = np.eye(n, dtype=bool)
-            result = FactState.FALSE if np.any(data * ~eye_mask) else FactState.TRUE
+            # Off-diagonal has a nonzero iff there are more nonzeros in ``data``
+            # than on its diagonal.
+            diag = np.diagonal(data, axis1=-2, axis2=-1)
+            if np.count_nonzero(data) == np.count_nonzero(diag):
+                result = FactState.TRUE
+            else:
+                result = FactState.FALSE
 
     var.tag.is_diagonal = result
     return result
diff --git a/pytensor/assumptions/permutation.py b/pytensor/assumptions/permutation.py
index bed9013a89..890f80fc89 100644
--- a/pytensor/assumptions/permutation.py
+++ b/pytensor/assumptions/permutation.py
@@ -38,13 +38,18 @@ def _permutation_from_constant(var: TensorConstant) -> FactState:
     if data.ndim < 2 or data.shape[-1] != data.shape[-2]:
         result = FactState.FALSE
     else:
-        # The row/column-sum reductions are cheaper and short-circuit the full-size binary
-        # scan; a doubly-stochastic matrix shows the binary check is still required.
-        is_permutation = (
-            bool(np.all(data.sum(axis=-2) == 1))
-            and bool(np.all(data.sum(axis=-1) == 1))
-            and bool(np.all((data == 0) | (data == 1)))
-        )
+        with np.errstate(invalid="ignore"):
+            if not (data.sum(axis=-2) == 1).all():
+                is_permutation = False
+            elif not (data.sum(axis=-1) == 1).all():
+                is_permutation = False
+            elif data.dtype.kind in "ub":
+                is_permutation = True
+            elif data.dtype.kind == "i":
+                is_permutation = data.min(initial=0) >= 0
+            else:
+                n = data.shape[-1]
+                is_permutation = np.count_nonzero(data) == (data.size // n if n else 0)
         result = FactState.TRUE if is_permutation else FactState.FALSE
 
     var.tag.is_permutation = result
diff --git a/pytensor/assumptions/selection.py b/pytensor/assumptions/selection.py
index 6698b3b29b..ee45479644 100644
--- a/pytensor/assumptions/selection.py
+++ b/pytensor/assumptions/selection.py
@@ -28,12 +28,18 @@ def _selection_from_constant(var: TensorConstant) -> FactState:
     if data.ndim < 2:
         result = FactState.FALSE
     else:
-        if not (data.sum(axis=-2) == 1).all():
-            is_selection = False
-        elif data.dtype.kind in "uib":
-            is_selection = data.max(initial=1) <= 1 and data.min(initial=0) >= 0
-        else:
-            is_selection = bool(((data == 0) | (data == 1)).all())
+        with np.errstate(invalid="ignore"):
+            if not (data.sum(axis=-2) == 1).all():
+                is_selection = False
+            elif data.dtype.kind in "ub":
+                is_selection = True
+            elif data.dtype.kind == "i":
+                is_selection = data.min(initial=0) >= 0
+            else:
+                n_rows = data.shape[-2]
+                is_selection = np.count_nonzero(data) == (
+                    data.size // n_rows if n_rows else 0
+                )
         result = FactState.TRUE if is_selection else FactState.FALSE
 
     var.tag.is_selection = result