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In this paper, we focus on Stochastic Amplitude Flow (SAF) for phaseretrieval, a stochastic gradient descent for the amplitude-based squared loss.While the convergence to a critical point of (nonstochastic) Amplitude Flow iswell-understood, SAF is a much less studied algorithm. We close this gap byderiving the convergence guarantees for SAF based on the contributions forAmplitude Flow and analysis for stochastic gradient descent. These results arethen applied to two more algorithms, which can be seen as instances of SAF. Thefirst is an extension of the Kaczmarz method for phase retrieval. The second isPtychographic Iterative Engine, which is a popular algorithm for ptychography,a special case of phase retrieval with the short-time Fourier transform.  Keywords: phase retrieval, Amplitude Flow, stochastic gradient descent,ptychography, Ptychographic Iterative Engine, Kaczmarz method.

Stochastic Amplitude Flow for phase retrieval, its convergence and doppelg\"angers