diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index b10d06120632..bf44d1176cc7 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2810,6 +2810,25 @@ def get_xlim(self):
         """
         return tuple(self.viewLim.intervalx)
 
+    def _validate_converted_limits(self, limit, convert):
+        """
+        Raise ValueError if converted limits are non-finite.
+
+        Note that this function also accepts None as a limit argument.
+
+        Returns
+        -------
+        The limit value after call to convert(), or None if limit is None.
+
+        """
+        if limit is not None:
+            converted_limit = convert(limit)
+            if (isinstance(converted_limit, float) and
+                    (not np.isreal(converted_limit) or
+                        not np.isfinite(converted_limit))):
+                raise ValueError("Axis limits cannot be NaN or Inf")
+            return converted_limit
+
     def set_xlim(self, left=None, right=None, emit=True, auto=False, **kw):
         """
         Set the data limits for the x-axis
@@ -2876,15 +2895,8 @@ def set_xlim(self, left=None, right=None, emit=True, auto=False, **kw):
             left, right = left
 
         self._process_unit_info(xdata=(left, right))
-        if left is not None:
-            left = self.convert_xunits(left)
-        if right is not None:
-            right = self.convert_xunits(right)
-
-        if ((left is not None and not np.isfinite(left)) or
-                (right is not None and not np.isfinite(right))):
-            raise ValueError("Specified x limits must be finite; "
-                             "instead, found: (%s, %s)" % (left, right))
+        left = self._validate_converted_limits(left, self.convert_xunits)
+        right = self._validate_converted_limits(right, self.convert_xunits)
 
         old_left, old_right = self.get_xlim()
         if left is None:
@@ -3175,15 +3187,8 @@ def set_ylim(self, bottom=None, top=None, emit=True, auto=False, **kw):
         if top is None and iterable(bottom):
             bottom, top = bottom
 
-        if bottom is not None:
-            bottom = self.convert_yunits(bottom)
-        if top is not None:
-            top = self.convert_yunits(top)
-
-        if ((top is not None and not np.isfinite(top)) or
-                (bottom is not None and not np.isfinite(bottom))):
-            raise ValueError("Specified y limits must be finite; "
-                             "instead, found: (%s, %s)" % (bottom, top))
+        bottom = self._validate_converted_limits(bottom, self.convert_yunits)
+        top = self._validate_converted_limits(top, self.convert_yunits)
 
         old_bottom, old_top = self.get_ylim()
 
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index 1f6637d206ad..2b44de576dc0 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -587,18 +587,6 @@ def _determine_lims(self, xmin=None, xmax=None, *args, **kwargs):
             xmax += 0.05
         return (xmin, xmax)
 
-    def _validate_axis_limits(self, limit, convert):
-        """
-        Raise ValueError if specified axis limits are infinite.
-
-        """
-        if limit is not None:
-            converted_limits = convert(limit)
-            if (isinstance(limit, float) and
-                    (not np.isreal(limit) or not np.isfinite(limit))):
-                raise ValueError("Axis limits cannot be NaN or Inf")
-            return converted_limits
-
     def set_xlim3d(self, left=None, right=None, emit=True, auto=False, **kw):
         """
         Set 3D x limits.
@@ -617,8 +605,8 @@ def set_xlim3d(self, left=None, right=None, emit=True, auto=False, **kw):
             left, right = left
 
         self._process_unit_info(xdata=(left, right))
-        left = self._validate_axis_limits(left, self.convert_xunits)
-        right = self._validate_axis_limits(right, self.convert_xunits)
+        left = self._validate_converted_limits(left, self.convert_xunits)
+        right = self._validate_converted_limits(right, self.convert_xunits)
 
         old_left, old_right = self.get_xlim()
         if left is None:
@@ -669,14 +657,14 @@ def set_ylim3d(self, bottom=None, top=None, emit=True, auto=False, **kw):
             bottom, top = bottom
 
         self._process_unit_info(ydata=(bottom, top))
-        if bottom is not None:
-            bottom = self.convert_yunits(bottom)
-        if top is not None:
-            top = self.convert_yunits(top)
+        bottom = self._validate_converted_limits(bottom, self.convert_yunits)
+        top = self._validate_converted_limits(top, self.convert_yunits)
 
         old_bottom, old_top = self.get_ylim()
-        bottom = self._validate_axis_limits(bottom, self.convert_yunits)
-        top = self._validate_axis_limits(top, self.convert_yunits)
+        if bottom is None:
+            bottom = old_bottom
+        if top is None:
+            top = old_top
 
         if top == bottom:
             warnings.warn(('Attempting to set identical bottom==top results\n'
@@ -721,8 +709,8 @@ def set_zlim3d(self, bottom=None, top=None, emit=True, auto=False, **kw):
             bottom, top = bottom
 
         self._process_unit_info(zdata=(bottom, top))
-        bottom = self._validate_axis_limits(bottom, self.convert_yunits)
-        top = self._validate_axis_limits(top, self.convert_yunits)
+        bottom = self._validate_converted_limits(bottom, self.convert_zunits)
+        top = self._validate_converted_limits(top, self.convert_zunits)
 
         old_bottom, old_top = self.get_zlim()
         if bottom is None: