WITH t(id,partition_id,data) AS (
  VALUES (1, 1, 'one'::text), (1, 2, NULL), (1, 3, NULL), (1, 4, 'two'),
         (2, 1, NULL), (2, 2, 'three'), (2, 3, NULL)
), u AS (
  SELECT *, max(data) OVER (PARTITION BY id, gg) filler FROM (
    SELECT *, sum(g) OVER (PARTITION BY id ORDER BY partition_id) gg FROM (
      SELECT *, CASE WHEN data IS NOT NULL AND data IS DISTINCT FROM lag(data) OVER (PARTITION BY id ORDER BY partition_id) THEN 1 END g FROM t
      ) x
    ) y
   ORDER BY id, partition_id
)
SELECT * FROM u;
--UPDATE t SET data=u.filler FROM u WHERE t.id=u.id AND t.partition_id=u.partition_id AND t.data IS NULL;