[qumpis]

What happens if we don't add any moments matching objective? e.g. at train time just fit a diffusion model that predicts the target given any pair of timesteps (t, t')? Why is moment matching critical here?

Also regarding linearity, why is it inflexible? It seems quite convenient that a simple linear interpolation is used for reconstruction, besides, even in DDIM, the directions towards the final target changes at each step as the images become less noisy. In standard diffusion models or even flow matching, denoising is always equal to the prediction of the original data + direction from current timestep to the timestep t'. Just to be clear, it is intuitive that such models are inferior in few-step generations since they don't optimise for test time efficiency (in terms of the tradeoff of quality vs compute), but it's unclear what inflexibility exists there beyond this limitation.

Clearly there's no expected benefit in quality if all timesteps are used in denoising?