  We derive a minimalist but powerful deterministic denoising-diffusion model.
While denoising diffusion has shown great success in many domains, its
underlying theory remains largely inaccessible to non-expert users. Indeed, an
understanding of graduate-level concepts such as Langevin dynamics or score
matching appears to be required to grasp how it works. We propose an
alternative approach that requires no more than undergrad calculus and
probability. We consider two densities and observe what happens when random
samples from these densities are blended (linearly interpolated). We show that
iteratively blending and deblending samples produces random paths between the
two densities that converge toward a deterministic mapping. This mapping can be
evaluated with a neural network trained to deblend samples. We obtain a model
that behaves like deterministic denoising diffusion: it iteratively maps
samples from one density (e.g., Gaussian noise) to another (e.g., cat images).
However, compared to the state-of-the-art alternative, our model is simpler to
derive, simpler to implement, more numerically stable, achieves higher quality
results in our experiments, and has interesting connections to computer
graphics.
