This project implements and extends a Linear Diffusion Model (LDM) for generative image modeling, developed as part of a coursework assignment .
Unlike standard diffusion models that rely heavily on deep neural networks, this model leverages classical machine learning techniques:
- One-hot encoded labels as prompts
- Principal Component Analysis (PCA) as the image encoder
- Multivariate Linear Regression as the denoiser
The purpose is to build a fully interpretable, lightweight diffusion model from linear components, capable of generating MNIST-like images from label prompts.
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Latent Diffusion in Linear Space
Diffusion is applied in a compressed PCA space, reducing training and generation costs. -
Nonlinear Encoders
PCA is replaced with alternatives like Kernel PCA or Random Fourier Features to introduce mild nonlinearity while avoiding neural networks. -
Cosine Variance Schedule
A noise schedule based on Nichol & Dhariwal (2021) improves sample quality over standard linear schedules. -
Accelerated Sampling
A strided sampling schedule reduces generation time significantly by sampling fewer diffusion steps. -
Empirical Evaluation
Image quality is assessed using: -
Pretrained MNIST classifiers
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Conformal prediction techniques to evaluate confidence and coverage
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Parameter Tuning
The model's behavior is studied under varying: -
Diffusion time
T -
Latent dimensionality
- MNIST: Used for training and classification
- Generated Dataset (Dn): Synthesized using the diffusion model, with balanced classes (e.g., 100 samples per digit)