feat: Improved DDPM Visualizations (arXiv:2102.09672)

[VicoErv]

Reference

Nichol & Dhariwal (2021) - Improved Denoising Diffusion Probabilistic Models
https://arxiv.org/abs/2102.09672

Overview

Implement interactive visualizations for key improvements from the Improved DDPM paper.

Features to Implement

1. Learnable Variance Schedule

• Visualize learned Σ_θ(x_t, t) vs fixed β_t
• Show sampling steps reduction (1000 → 50 steps)
• Interactive comparison mode

2. Cosine Noise Schedule

• Plot cosine vs linear ᾱ_t schedules
• Toggle between schedules in Point Cloud Diffusion
• Show visual impact on noise progression

3. Hybrid Loss Objective

• Visualize L_hybrid = L_simple + λ*L_vlb
• Interactive λ slider
• Show loss component breakdown

4. Full Reverse Sampling Process

• Step-by-step denoising visualization (x_T → x_0)
• Real-time formula evaluation
• Adjustable sampling steps

Acceptance Criteria

• All 4 visualization components implemented
• Interactive controls for each feature
• LaTeX formula rendering
• Integration with existing Point Cloud Diffusion lab