  We present a fresh perspective on shot noise corrupted images and noise
removal. By viewing image formation as the sequential accumulation of photons
on a detector grid, we show that a network trained to predict where the next
photon could arrive is in fact solving the minimum mean square error (MMSE)
denoising task. This new perspective allows us to make three contributions: We
present a new strategy for self-supervised denoising, We present a new method
for sampling from the posterior of possible solutions by iteratively sampling
and adding small numbers of photons to the image. We derive a full generative
model by starting this process from an empty canvas. We call this approach
generative accumulation of photons (GAP). We evaluate our method quantitatively
and qualitatively on 4 new fluorescence microscopy datasets, which will be made
available to the community. We find that it outperforms supervised,
self-supervised and unsupervised baselines or performs on-par.
