Beyond Layers: Continuous Normalizing Flows with Neural ODEs

This repository contains the PyTorch implementation for training a Continuous Normalizing Flow (CNF) to solve density estimation on the "Two Moons" dataset. It utilizes the TorchDyn library to handle ODE integration and the Adjoint Sensitivity Method.

Read the Blog Series

This code accompanies my article series "Beyond Layers", where I explain the intuition and mathematics behind Neural ODEs.

• Part 1: The Intuition Behind Neural ODEs - Moving from discrete layers to continuous dynamics.
• Part 2: Implementing Continuous Normalizing Flows - A practical guide to training CNFs for generative modeling.

Results

1. Generative Sampling (Reverse Flow)

Transforming a standard Gaussian distribution ($t=1$) back into the complex Two Moons data distribution ($t=0$) by integrating the learned vector field backward in time.

(Above: A GIF of the learned flow carrying noise particles to the data manifold)

2. Learned Density

The model successfully learned a continuous probability density function that matches the geometry of the target dataset.

3. Training Convergence

The model minimizes the Negative Log-Likelihood (NLL) effectively over 250 epochs.

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Installation & Usage

1. Clone the repository

   git clone https://github.com/vaishnavibiradar/beyond-layers-cnf.git
   cd beyond-layers-cnf