Blind diffuser-modulation ptychography has emerged as a low-cost technique for micro-nano holographic imaging, which enables breaking the resolution limit of optical systems. However, the existing reconstruction method requires thousands of measurements to recover object and diffuser profile simultaneously, which makes the data acquisition time-consuming and cumbersome. In this Letter, we report a novel, to the best of our knowledge, blind ptychography technique with deep distributed optimization, termed BPD2O. It decomposes the complicated optimization task into subproblems, then introduces extended ptychographical iterative engine and enhanced network solver to optimize each in a distributed strategy. In this way, BPD2O combines the advantages of both model-driven and data-driven strategies, realizing high-fidelity robust ptychography imaging. Extensive experiments validate that BPD2O can realize better resolution and lead to a reduction of more than one order of magnitude in the number of measurements.