SUM() と JOIN を使えば書ける．JOIN してるのでオーダーは小さくなさそうな気がする． COUNT(*) をよしなに所望のものに変えれば好きなものの累積和が取れる．テーブル名なども適宜読み替えてください．

SELECT
    t1.accum_date
  , t1.count
  , t1.count + SUM(t2.count) AS accum
FROM (
    SELECT
        DATE(created_at) AS accum_date
      , COUNT(*) AS count
    FROM
        images
    GROUP BY accum_date
    ORDER BY accum_date
) AS t1
JOIN (
    SELECT
        DATE(created_at) AS accum_date
      , COUNT(*) AS count
    FROM
        images
    GROUP BY accum_date
    ORDER BY accum_date
) AS t2
ON
    t1.accum_date > t2.accum_date
WHERE
    t1.accum_date >= TIMESTAMP '2012-07-01 00:00:00'
AND t1.accum_date < TIMESTAMP '2017-09-01 00:00:00'
GROUP BY t1.accum_date
ORDER BY t1.accum_date