Part 4 · The Maths II: Masked Discrete Diffusion
Where the speed–quality trade-off lives, formally
To generate with T steps, discretize t = 1 → 0 and repeatedly apply the reverse posterior with xθ substituted for x. Within one step, each masked position reveals independently with probability (αs−αt)/(1−αt), each sampling from its own marginal — the mean-field approximation from the Intuition section, now with coordinates. As T → ∞ the per-step reveal probability shrinks until at most one token flips per step and the factorization becomes exact; small T means many simultaneous, uncoordinated reveals. The step count is precisely the dial on mean-field error.
The modern extensions — Block Diffusion, ReMDM, guidance, diffu-GRPO — each modify exactly one piece of the machinery above. Their equations get their own section next.