Generative Modeling
Denoising Score Matching Intuition - Vectors point from corrupted samples back to clean data, approximating the score

A Connection Between Score Matching and Denoising Autoencoders

Theoretical paper proving the equivalence between training Denoising Autoencoders and performing Score Matching on a …

Machine Learning Fundamentals
Comparison of linear interpolation (teleportation) showing double peaks versus displacement interpolation (transportation) showing smooth single peak

A Convexity Principle for Interacting Gases

Introduces displacement interpolation to prove ground state uniqueness via optimal transport, establishing foundations …

Generative Modeling
Visualization of probability density flow from initial distribution ρ₀ to target distribution ρ₁ over time through space

Building Normalizing Flows with Stochastic Interpolants

A continuous-time normalizing flow using stochastic interpolants and quadratic loss to bypass costly ODE …

Generative Modeling
Visualization comparing Optimal Transport (straight paths) vs Diffusion (curved paths) for Flow Matching

Flow Matching for Generative Modeling

A simulation-free framework for training Continuous Normalizing Flows using Conditional Flow Matching and Optimal …

Generative Modeling
Visualization showing linear interpolation, learned ODE trajectories, and the reflow straightening process for rectified flow

Flow Straight and Fast

A unified ODE-based framework for generative modeling and domain transfer that learns straight paths for fast 1-step …

Machine Learning Fundamentals
Comparison of Residual Network vs ODE Network architectures showing discrete layers versus continuous transformations

Neural Ordinary Differential Equations

Introduces ODE-Nets, a continuous-depth neural network model parameterized by ODEs, enabling constant memory …

Generative Modeling
Forward and Reverse SDE trajectories showing the diffusion process from data to noise and back

Score-Based Generative Modeling with SDEs

Unified SDE framework for score-based generative models, introducing Predictor-Corrector samplers and achieving SOTA on …

Machine Learning Fundamentals
Visualization of inverse problem showing one input mapping to multiple valid outputs

Mixture Density Networks

Seminal 1994 paper introducing MDNs to model arbitrary conditional probability distributions using neural networks.

Generative Modeling
Diagram comparing standard stochastic sampling (gradient blocked) vs the reparameterization trick (gradient flows)

Auto-Encoding Variational Bayes (VAE Paper Summary)

Summary of Kingma & Welling's foundational VAE paper introducing the reparameterization trick and variational …

Generative Modeling
Flowchart comparing VAE and IWAE computation showing the key difference in where averaging occurs relative to the log operation

IWAE: Importance Weighted Autoencoders

Summary of Burda, Grosse & Salakhutdinov's ICLR 2016 paper introducing Importance Weighted Autoencoders for tighter …

Generative Modeling
Visualization of the VAE prior hole problem showing a ring-shaped aggregate posterior with an empty center where the Gaussian prior has highest density

Contrastive Learning for Variational Autoencoder Priors

Aneja et al.'s NeurIPS 2021 paper introducing Noise Contrastive Priors (NCPs) to address VAE's 'prior hole' problem with …