Generative Models

Jul 30, 2025 Standalone 26 min read

Reparameterization Trick & Gumbel-Softmax: A Deep Dive

Make sense of the reparameterization trick and Gumbel-Softmax: why gradients can flow through sampling, how temperature trades bias for variance, and the practical pitfalls of training discrete latent variables …

Jul 30, 2024 PDE and Machine Learning 38 min read

PDE and ML (7): Diffusion Models and Score Matching

Diffusion models are PDE solvers in disguise. We derive the heat equation, Fokker-Planck, score matching, DDPM, and DDIM from a unified PDE perspective and visualise every step.

Jun 27, 2023 Standalone 24 min read

Variational Autoencoder (VAE): From Intuition to Implementation and Troubleshooting

Build a VAE from scratch in PyTorch. Covers the ELBO objective, reparameterization trick, posterior collapse fixes, beta-VAE, and a complete training pipeline.