Step-by-Step Diffusion: An Elementary Tutorial
by Preetum Nakkiran, Arwen Bradley, Hattie Zhou, Madhu Advani · arXiv
A 35-page tutorial deriving diffusion models and flow matching from first principles, deliberately avoiding SDEs, ELBOs and score functions. Assumes probability, calculus and linear algebra, and gives pseudocode for the sampling algorithms it derives. The single best free entry point to the mathematics. Needs no stochastic calculus or variational-bound machinery, so a reader with undergraduate probability can follow a complete derivation of DDPM and DDIM sampling and then implement it.
More resources on Generative Image & Video Models
Extracting Training Data from Diffusion Models
A USENIX Security 2023 study that recovers over a thousand memorized training images from Stable Diffusion, Imagen and DALL-E 2, including photographs of identifiable people and trademarked logos, and measures which design choices worsen memorization. It quantifies how often models reproduce training images and reports the copyright status of what it extracted.
Hands-On Generative AI with Transformers and Diffusion Models
A practitioner's book from the Hugging Face Diffusers team covering how diffusion models work, Stable Diffusion internals, sampling and guidance, fine-tuning with LoRA and DreamBooth, ControlNet and inpainting workflows, and chapters on audio and video generation.
Practical Deep Learning for Coders, Part 2: From Deep Learning Foundations to Stable Diffusion
Over thirty hours of free video lessons rebuilding Stable Diffusion from scratch, starting at matrix multiplication and autograd and working up through DDPM, DDIM, conditional sampling, textual inversion and DreamBooth, with paper-reading practice throughout. The only free course taking a reader from tensor primitives to a working diffusion implementation without hand-waving, and the depth means the understanding survives model churn. Long and demanding.
Hugging Face Diffusers Documentation
Official documentation for the Diffusers library: pipelines for image, video and audio generation, scheduler choices, LoRA and adapter loading, ControlNet usage, DreamBooth and textual-inversion training scripts, quantization and memory-offloading guides, and conceptual explanations of each component. The practical half of the topic — running models, choosing schedulers, applying LoRA and ControlNet, fine-tuning — has no better free source, and the maintainers' own docs avoid the huge volume of blog tutorials written against long-dead API versions.
Adding Conditional Control to Text-to-Image Diffusion Models (ControlNet)
The paper introducing ControlNet, which adds spatial conditioning such as edges, depth, segmentation and human pose to a frozen text-to-image diffusion model using trainable copies of its encoder joined by zero-initialized convolutions.
High-Resolution Image Synthesis with Latent Diffusion Models
The CVPR 2022 paper behind Stable Diffusion. It runs the diffusion process in the latent space of a pretrained autoencoder and adds cross-attention conditioning, cutting compute enough for consumer hardware while handling text, layout, inpainting and super-resolution. Every practical tool in this topic — SD 1.5, SDXL, and their descendants — is an implementation of this paper.