FromMathToMagic-SOC

Summer of Code repository documenting my implementation journey from the mathematical foundations of probabilistic models to the forward diffusion process used in Denoising Diffusion Probabilistic Models (DDPMs).

This repository contains weekly notebooks, experiments, visualizations, and implementations completed during the first eight weeks of the project.

Overview

This repository documents my Summer of Code learning journey covering:

• Probability and Statistics
• Gaussian Distributions
• Bayes' Theorem
• KL Divergence
• Evidence Lower Bound (ELBO)
• Variational Autoencoders (VAE)
• Convolutional VAEs
• Latent Space Analysis
• Denoising Diffusion Probabilistic Models (DDPM)
• Forward Diffusion Process
• Linear and Cosine Noise Schedules
• PyTorch Implementations

Repository Structure

Week0/
Week1/
Week2/
Week3/
Week4/
Week5/
Week6/
Week7/
Week8/

Weekly Progress

Week 0 – Onboarding

• Python and PyTorch fundamentals
• Neural network training workflow
• Linear regression implementation

Week 1 – The Math of Uncertainty

• Gaussian distributions
• Bayes' theorem
• KL divergence
• Probabilistic modeling foundations

Week 2 – ELBO and KL Divergence

• Derived and implemented KL divergence
• Verified ELBO components
• Worked with latent variable formulations

Week 3 – Variational Autoencoder

• Implemented a fully connected VAE
• Trained on MNIST
• Visualized latent representations

Week 4 – Convolutional VAE

• Built a ConvVAE using convolutional layers

• Generated and reconstructed MNIST digits

• t-SNE visualization of latent space

• Latent space interpolation

• β-VAE experiments

• Week 5 – Dataset Preparation

• Prepared CelebA dataset

• Built custom PyTorch Dataset loader

• Image preprocessing

• Data pipeline setup

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Week 6 – Forward Diffusion Implementation

• Implemented reusable ForwardDiffusion class
• Linear beta schedule
• Cosine beta schedule
• Closed-form forward diffusion equation

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Week 7 – Numerical Verification & Visualization

• Verified forward diffusion mathematically
• Generated diffusion trajectory
• Created destruction GIF
• Visualized gradual image corruption

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Week 8 – Noise Schedule Comparison

• Compared Linear vs Cosine schedules
• Studied effect on image degradation
• Completed reusable notebook for forward diffusion pipeline

Tools Used

• Python

• NumPy

• PyTorch

• Matplotlib

• Pillow

• imageio

• Google Colab

• Git

• GitHub

• Project Status

Current Progress: Week 8 / Week 13

Completed:

• Mathematical foundations
• Variational Autoencoders
• Forward Diffusion Process
• Noise Schedule Analysis

Upcoming Work:

• Reverse Diffusion

• U-Net implementation

• Noise Prediction Network

• Image Generation

• Conclusion

This repository documents my Summer of Code journey from foundational probability concepts to implementing the forward diffusion process used in DDPMs. Throughout the first eight weeks, I progressively built the theoretical understanding and practical implementation required for diffusion models. The remaining weeks will focus on reverse diffusion, neural network training, and image generation to complete the full DDPM pipeline.

Author

Diptanshu Raut
B.Tech Chemical Engineering, IIT Bombay