diff --git a/umap/umap_.py b/umap/umap_.py
index 52c3a280..695f0bf8 100644
--- a/umap/umap_.py
+++ b/umap/umap_.py
@@ -1044,18 +1044,24 @@ def simplicial_set_embedding(
     graph.sum_duplicates()
     n_vertices = graph.shape[1]
 
-    if n_epochs <= 0:
-        # For smaller datasets we can use more epochs
-        if graph.shape[0] <= 10000:
-            n_epochs = 500
-        else:
-            n_epochs = 200
+    # For smaller datasets we can use more epochs
+    if graph.shape[0] <= 10000:
+        default_epochs = 500
+    else:
+        default_epochs = 200
 
-        # Use more epochs for densMAP
-        if densmap:
-            n_epochs += 200
+    # Use more epochs for densMAP
+    if densmap:
+        default_epochs += 200
+
+    if n_epochs is None:
+        n_epochs = default_epochs
+
+    if n_epochs > 10:
+        graph.data[graph.data < (graph.data.max() / float(n_epochs))] = 0.0
+    else:
+        graph.data[graph.data < (graph.data.max() / float(default_epochs))] = 0.0
 
-    graph.data[graph.data < (graph.data.max() / float(n_epochs))] = 0.0
     graph.eliminate_zeros()
 
     if isinstance(init, str) and init == "random":
@@ -1702,9 +1708,9 @@ def _validate_parameters(self):
         if self.n_components < 1:
             raise ValueError("n_components must be greater than 0")
         if self.n_epochs is not None and (
-            self.n_epochs <= 10 or not isinstance(self.n_epochs, int)
+            self.n_epochs < 0 or not isinstance(self.n_epochs, int)
         ):
-            raise ValueError("n_epochs must be a positive integer of at least 10")
+            raise ValueError("n_epochs must be a nonnegative integer")
         if self.metric_kwds is None:
             self._metric_kwds = {}
         else:
@@ -2567,11 +2573,6 @@ def fit(self, X, y=None):
         else:
             self._supervised = False
 
-        if self.n_epochs is None:
-            n_epochs = 0
-        else:
-            n_epochs = self.n_epochs
-
         if self.densmap or self.output_dens:
             self._densmap_kwds["graph_dists"] = self.graph_dists_
 
@@ -2581,7 +2582,7 @@ def fit(self, X, y=None):
         if self.transform_mode == "embedding":
             self.embedding_, aux_data = self._fit_embed_data(
                 self._raw_data[index],
-                n_epochs,
+                self.n_epochs,
                 init,
                 random_state,  # JH why raw data?
             )