In-depth analysis of the Flow Matching training algorithm. 🎮 Companion interactive tutorial (free, no sign-in): https://diffusion.fyi ▶️ Diffusion models playlist: https://youtube.com/playlist?list=PL4bm2lr9UVG3SN79Y6WBe4OOlEiO88vie&si=S6yXhaPK-H0T75MA 📚 Papers: (These are concurrent works, all credited for the algorithm) Flow Matching: https://arxiv.org/abs/2210.02747 Rectified Flow: https://arxiv.org/abs/2209.03003 Stochastic Interpolants: https://arxiv.org/abs/2209.15571 00:00 Intro 01:13 Time-variant probability density 03:37 The continuity equation 04:34 Time-variant velocity field 06:42 Flow-based methods 07:30 Continuous Normalizing Flow 08:30 Flow Matching loss 09:39 FM end-to-end algorithm 11:23 Conditional velocity fields 13:26 Optimal transport 16:24 Why are velocity labels constant? 18:23 Conflicting velocity labels 22:02 Rectified Flow