扩散概率模型：理论与应用-英-43页

DiffusionProbabilisticModels:TheoryandApplicationsFanBaoTsinghuaUniversityByFanBao,TsinghuaUniversity1DiffusionProbabilisticModels(DPMs)Hoetal.Denoisingdiffusionprobabilisticmodels(DDPM),Neurips2020.Songetal.Score-basedgenerativemodelingthroughstochasticdifferentialequations,ICLR2021.Baoetal.Analytic-DPM:anAnalyticEstimateoftheOptimalReverseVarianceinDiffusionProbabilisticModels,ICLR2022.Baoetal.EstimatingtheOptimalCovariancewithImperfectMeaninDiffusionProbabilisticModels,ICML2022.ByFanBao,TsinghuaUniversity2•Diffusionprocessgraduallyinjectsnoisetodata•DescribedbyaMarkovchain:𝑞𝑥0,…,𝑥𝑁=𝑞𝑥0𝑞𝑥1𝑥0…𝑞(𝑥𝑁𝑥𝑁−1)Transitionofdiffusion:𝑞𝑥𝑛𝑥𝑛−1=𝑁(𝛼𝑛𝑥𝑛−1,𝛽𝑛𝐼)𝛼𝑛=1−𝛽𝑛𝑥0𝑥1𝑥2…𝑥𝑁≈𝑁(0,𝐼)Diffusionprocess:𝑞𝑥0,…,𝑥𝑁=𝑞𝑥0𝑞𝑥1𝑥0…𝑞(𝑥𝑁𝑥𝑁−1)DemoImagesfromSongetal.Score-basedgenerativemodelingthroughstochasticdifferentialequations,ICLR2021.ByFanBao,TsinghuaUniversity3•Diffusionprocessinthereversedirection⇔denoisingprocess•Reversefactorization:𝑞𝑥0,…,𝑥𝑁=𝑞𝑥0𝑥1…𝑞𝑥𝑁−1𝑥𝑁𝑞(𝑥𝑁)Transitionofdenoising:𝑞𝑥𝑛−1𝑥𝑛=?𝑥0𝑥1𝑥2…𝑥𝑁≈𝑁(0,𝐼)Diffusionprocess:𝑞𝑥0,…,𝑥𝑁=𝑞𝑥0𝑞𝑥1𝑥0…𝑞(𝑥𝑁𝑥𝑁−1)=𝑞𝑥0𝑥1…𝑞𝑥𝑁−1𝑥𝑁𝑞(𝑥𝑁)ByFanBao,TsinghuaUniversity4•ApproximatediffusionprocessinthereversedirectionModeltransition:𝑝𝑥𝑛−1𝑥𝑛=𝑁(𝜇𝑛𝑥𝑛,Σ𝑛(𝑥𝑛))approx...