diff --git a/sc2ts/inference.py b/sc2ts/inference.py
index b02cdb2..af3abb3 100644
--- a/sc2ts/inference.py
+++ b/sc2ts/inference.py
@@ -1424,7 +1424,17 @@ def trim_branches(ts):
     return tables.tree_sequence()
 
 
-def attach_tree(parent_ts, parent_tables, attach_path, reversions, child_ts, date):
+def attach_tree(
+    parent_ts,
+    parent_tables,
+    attach_path,
+    reversions,
+    child_ts,
+    date,
+    epsilon=None,
+):
+    if epsilon is None:
+        epsilon = 1e-6  # In time units of days ago
 
     root_time = min(parent_ts.nodes_time[seg.parent] for seg in attach_path)
     if root_time == 0:
@@ -1444,19 +1454,37 @@ def attach_tree(parent_ts, parent_tables, attach_path, reversions, child_ts, dat
         child_ts = add_root_edge(child_ts)
         tree = child_ts.first()
 
+    # Add sample node times
+    current_date = parse_date(date)
+    node_time = {}  # In time units of days ago
+    for u in tree.postorder():
+        if tree.is_sample(u):
+            node = child_ts.node(u)
+            sample_date = parse_date(node.metadata['date'])
+            node_time[u] = (current_date - sample_date).days
+            assert node_time[u] >= 0.0
+    max_sample_time = max(node_time.values())
+
     node_id_map = {}
     if child_ts.nodes_time[tree.root] != 1.0:
         raise ValueError("Time must be scaled from 0 to 1.")
-    node_time = {}
+
+    num_internal_nodes_visited = 0
     for u in tree.postorder()[:-1]:
         node = child_ts.node(u)
-        # Tree branch length is scaled from 0 to 1.
-        time = node.time * root_time
-        node_time[u] = time
+        if tree.is_sample(u):
+            # All sample nodes are terminal
+            time = node_time[u]
+        else:
+            num_internal_nodes_visited += 1
+            time = max_sample_time + num_internal_nodes_visited * epsilon
+            node_time[u] = time
         metadata = node.metadata
         if tree.is_internal(u):
             metadata = {"date_added": date}
-        new_id = parent_tables.nodes.append(node.replace(time=time, metadata=metadata))
+        new_id = parent_tables.nodes.append(
+            node.replace(time=time, metadata=metadata)
+        )
         node_id_map[node.id] = new_id
         for v in tree.children(u):
             parent_tables.edges.add_row(