Flow-based generative models are a powerful class of deep generative models, and in this video, we dive into Continuous Normalizing Flows (CNF)-an extension that leverages Neural ODEs to model complex distributions with continuous transformations.

We start by exploring vector fields and ordinary differential equations (ODEs), then implement simple yet effective CNFs that transform samples from a simple distribution like a standard normal into target distributions. Along the way, we discuss techniques like the Euler method, the adjoint method, and trace estimation—key concepts that make continuous flow modeling computationally feasible.

⏱️ Timestamps
00:00 Intro
00:32 – Vector Fields and Ordinary Differential Equation
09:41 – Euler Method for Solving ODE
12:03 – Neural ODE
19:16 – PyTorch implementation of Continuous Normalizing Flows Model
26:33 – Adjoint and Trace Estimation

📖 Resources
Neural ODE Paper - https://arxiv.org/pdf/1806.07366
Adjoint Proof - https://youtu.be/Keo3sVjFjOU?list=TLPQMjQwOTIwMjUJBxxWr7J8qQ&t=3084
Adjoint Playlists
1. https://www.youtube.com/playlist?list=PLcqHTXprNMIMinq16VTi6cFeTxuEqlqHC
2. https://www.youtube.com/playlist?list=PLISXH-iEM4Jk27AmSvISooRRKH4WtlWKP

💡Credits
The animations for vector fields were based on amazing 3blue1brown videos specifically his animations in video on Divergence and Curl(where he also talked about vector field).

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