DDPM:Lower bound of logP(x) VAE Maximize logPa(x) Maximize☑[log P(,Z q☑x) Encoder DDPM Maximize logPe(xo) Maximize q(x log P(xo:xT q(x:xrlxo) Forward Process (Diffusion Process) q(x1:xTlxo)=q(xilxo)q(x21x1)...q(xrlxT-1)
DDPM: Lower bound of 𝑙𝑜𝑔𝑃 𝑥 Maximize 𝑙𝑜𝑔𝑃𝜃 𝑥0 Maximize E𝑞 𝑥1:𝑥𝑇|𝑥0 [𝑙𝑜𝑔 𝑃 𝑥0: 𝑥𝑇 𝑞 𝑥1: 𝑥𝑇|𝑥0 ] Maximize 𝑙𝑜𝑔𝑃𝜃 𝑥 Maximize E𝑞 𝑧|𝑥 [𝑙𝑜𝑔 𝑃 𝑥, 𝑧 𝑞 𝑧|𝑥 ] Encoder Forward Process (Diffusion Process) VAE DDPM 𝑞 𝑥1: 𝑥𝑇|𝑥0 = 𝑞 𝑥1|𝑥0 𝑞 𝑥2|𝑥1 … 𝑞 𝑥𝑇|𝑥𝑇−1
q(xtlxt-1) ~N(0,I) V1-B: Xt-1 Xt β1β2，…，βT q(xtlxo) weeeee
+ + + …… = 𝛽1, 𝛽2, … , 𝛽𝑇 1 − 𝛽𝑡 + 𝛽𝑡 ~𝒩 𝟎,𝐼 𝑞 𝑥𝑡 |𝑥𝑡−1 𝑥𝑡−1 𝑥𝑡 𝑞 𝑥𝑡 |𝑥0 𝑥0 𝑥𝑡