【AI論文解説】Consistency ModelとRectified Flow
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YouTube nnabla channelの次の動画で利用したスライドです。 【AI論文解説】Consistency ModelとRectified Flow https://youtu.be/3IKCrAPe55k Consistency ModelとRectified Flowに関連する以下の論文を紹介しています。 Consistency models（解説編Part1で紹介） - “Consistency Models,” ICML 2023. - “Improved Techniques for Training Consistency Models,” ICLR 2024. - “Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion,” ICLR 2024. Rectified flow（解説編Part2で紹介） - “Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow,” ICLR 2023. - “InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation,” ICLR 2024.
【AI論文解説】Consistency ModelとRectified Flow
- 4. • 𝑝(𝑧) 𝑝(𝑥)
- 5. • 𝑝(𝑧) 𝑝(𝑥)
- 6. •
- 7. •
- 8. • •
- 9. • d𝐱𝑡 d𝑡 d𝐱𝑡 = 2𝑡 d𝒘𝑡 d𝐱𝑡 = −𝑡∇𝐱 log𝑝𝑡(𝐱) d𝑡
- 11. •
- 12. •
- 14. ⇒
- 15. •
- 16. • 𝑓𝜽 𝐱, 0 = 𝐱 𝑓𝜽 𝐱𝑡, 𝑡 = 𝑓𝜽 𝐱𝑡−Δ𝑡, 𝑡 − Δ𝑡 𝑓𝜽 𝐱𝑡,𝑡 𝑓𝜽 𝐱𝑡−1,𝑡 − Δ𝑡
- 17. • ℒ𝐶𝐷 𝑁 (𝜽,𝜽−) = 𝔼𝐱,𝝐,𝑛 𝜆 𝑡𝑛 𝑑 𝑓𝜽 𝐱𝑡𝑛+1 , 𝑡𝑛+1 , 𝑓𝜽− ො 𝐱𝑡𝑛 𝝓 , 𝑡𝑛
- 18. • ℒ𝐶𝑇 𝑁 (𝜽,𝜽−) = 𝔼𝐱,𝝐,𝑛 𝜆 𝑡𝑛 𝑑 𝑓𝜽 𝐱 + 𝑡𝑛+1𝝐, 𝑡𝑛+1 , 𝑓𝜽− 𝐱 + 𝑡𝑛𝝐, 𝑡𝑛 ℒ𝐶𝐷 𝑁 𝜽,𝜽− = ℒ𝐶𝑇 𝑁 𝜽,𝜽− + 𝑜(Δ𝑡)
- 19. • • 𝐱𝑡 𝐱𝑡
- 20. •
- 21. • • •
- 22. • • •
- 23. • • • ⇒
- 24. • • ⇒ ⇒
- 25. •
- 26. • 𝑓𝜽 𝐱𝑡,𝑡,𝑠 𝑓𝜽 𝐱𝑡−1,𝑡 − Δ𝑡, 𝑠 𝐱𝑠 𝑠 = 𝑡 − Δ𝑡 𝑠 = 0
- 27. •
- 28. •
- 29. •
- 30. •
- 31. • •
- 32. •
- 34. • 𝐱𝑡 = 𝑡𝐱1 + (1 − 𝑡)𝐱0 d𝐱𝑡 = 𝐱1 − 𝐱0 d𝑡 𝐱𝑡
- 35. d𝐱𝑡 = 𝐱1 − 𝐱0 d𝑡 d𝐱𝑡 = 𝑣𝜽(𝐱𝑡,𝑡)d𝑡 min 𝜽 න 0 1 𝔼𝐱0,𝐱1 𝐱1 − 𝐱0 − 𝑣𝜽 𝐱𝑡,𝑡 2 d𝑡 𝐱𝑡 𝐱𝑡
- 37. • (𝐱0, 𝐱1) ⇒ 𝐱𝑡
- 38. • • (𝐱0 𝑘 , 𝐱1 𝑘 ) • • 𝐱1 𝑘 ≈ 𝐱0 𝑘 + 𝑣𝜽 𝐱0,0 min 𝜽 𝔼(𝐱0 𝑘 ,𝐱1 𝑘 ) 𝐱1 𝑘 − 𝐱0 𝑘 − 𝑣𝜽 𝐱0 𝑘 ,0 2
- 39. •
- 40. •
- 42. •
- 43. • • • 𝜖𝜽 𝛾 = 𝜖𝜽 𝐱𝑡, 𝑡, NULL + 𝛾 𝜖𝜽 𝐱𝑡, 𝑡, 𝒯 − 𝜖𝜽(𝐱𝑡, 𝑡, NULL) (𝐱0,𝐱1) 𝛾 = 5.0 𝛾 = 5.0 𝛾 = 1.5 𝛾 = 1.5
- 44. • • • •
- 45. •
- 47. • • • • • • •
- 48. • • • min 𝜽 𝔼𝑡,𝐱0,𝐱1 𝐱1 − (1 − 𝜎min)𝐱0 − 𝑣𝜽 𝐱𝑡,𝑡 2 𝐱𝑡 = 1 − 1− 𝜎min 𝑡 𝐱0 + 𝑡𝐱1 ≈ =
- 49. • • • • 𝐱𝑡 = 𝑡𝐱 + 1 − 𝑡 𝝐 𝐱𝑡 = ത 𝛼𝑡𝐱 + 1 − ത 𝛼𝑡𝝐 𝐱𝑡 = 𝐱 + 𝜎𝑡𝝐 𝐱 − 𝝐 𝝐 𝐱 𝒗