Blog Series

A Probabilistic Modeling Route from ELBO and Score Matching to Velocity Fields: Notes and Summary

This series organizes a mathematically coherent route that starts from latent variable models, passes through ELBO, VAE, hierarchical latent variables, DDPM variational bounds, denoising score matching, SDE / probability flow ODE, and continuous normalizing flow, and finally arrives at the flow matching objective.

1. Latent Variable and ELBO latent variable -> ELBO 2. VAE and Hierarchical Latent Variable VAE -> hierarchy 3. DDPM Variational Bound diffusion as variational inference 4. Denoising Score Matching score estimation 5. SDE and Probability Flow ODE stochastic to deterministic flow 6. Continuous Normalizing Flow change of variables in time 7. Flow Matching Objective velocity field learning