Diffusion Models Explained: Mathematics Behind Stable Diffusion, VAEs, U-Nets, and LoRA

Diffusion models are the foundation of modern image generation systems such as Stable Diffusion. In this video, we take a deep yet intuitive dive into how diffusion models actually work, both conceptually and mathematically.
We begin with the core idea of diffusion: the forward process, where images are gradually corrupted into pure Gaussian noise, and the reverse process, where a neural network learns to denoise step by step and recover the original image. From there, we move beyond intuition and unpack the underlying learning objective that makes this possible.

The video explains how Variational Autoencoders (VAEs) compress high-dimensional images into a latent space for efficient training, and why U-Net architectures are so effective at preserving spatial structure during denoising. We then connect these architectural choices to the mathematics, showing how variational inference, the Evidence Lower Bound (ELBO), and score-based generative modeling all describe the same training process from different perspectives.

Practical techniques used in real-world systems are also covered, including Classifier-Free Guidance for stronger text–image alignment and LoRA (Low-Rank Adaptation) for efficient fine-tuning and style control. Throughout the video, the goal is to bridge high-level creative intuition with the rigorous probability theory and stochastic processes that make diffusion models work in practice.

Видео Diffusion Models Explained: Mathematics Behind Stable Diffusion, VAEs, U-Nets, and LoRA канала Vikram Lingam