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Advanced•Modern AI
Flow Matching & DiT Video
Rectified Flow matching, optimal transport vector fields, and Patchified Diffusion Transformers (Sora/Flux).
Interactive Playground
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Research-Level Deep Dive & Equations
Classical generative diffusion models (DDPM/DDIM) construct probability paths by gradually adding Gaussian noise to clean data via a forward Stochastic Differential Equation (SDE):
•The Limitations of Stochastic SDEs: Because the forward noise path adds random Brownian motion , the resulting reverse sampling trajectories are heavily curved and noisy. Generating samples requires **50 to 100 NFE (Number of Function Evaluations)** numerical ODE steps.
•Continuous Flow Matching Paradigm: Lipman et al. (2022) and Albergo & Vanden-Eijnden (2022) formulated generative modeling as learning a deterministic vector field that generates an Ordinary Differential Equation (ODE) probability flow:
pushing a simple base noise distribution at to the complex data distribution at .
Key Equations
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