Each forward step multiplies the data by √(1−β_t) and adds Gaussian noise with variance β_t. Unrolled, x_t = √ᾱ_t·x_0 + √(1−ᾱ_t)·ε̂_t, and nothing here is learned. The reverse direction is learned with a Gaussian p_θ(x_{t−1}|x_t): apply last lecture's ELBO to the whole trajectory, split it with the KL chain rule, and the loss at each step is ‖μ̃_t(x_t,x_0) − μ_θ(x_t,t)‖²/(2β̃_t). The lecture stops at this expression; simplifying it into noise prediction is left for Lecture 12.
The first half collapses the diffusion ELBO into one expression: every time step is a squared error for guessing the noise that was added, which gives a five-step training procedure and a one-loop sampler. The second half opens the foundation-model unit: the two-stage paradigm of pretraining plus adaptation, linear probe, finetune, LP-FT, and why LoRA trains only 2dr parameters yet saves very little compute.
Audio representation, temporal relationships in video, and action-conditioned world transitions are different learning tasks. The earlier combined guide checked only audio at the end. This URL now serves as a reading map to one full guide each for Lectures 24–26; the Lecture 26 guide also covers the separate alignment deck.
Cross-attention reads another representation, DiT is a diffusion-backbone choice, and Q-Former uses learned queries to extract or bridge information. They can coexist rather than being three competing products. The Lecture 14 lesson handles Prompt-to-Prompt and classifier-free guidance in detail.
Diffusion and VAEs share probabilistic ideas without sharing the same generation procedure. Diffusion chains noise steps; a VAE approximates a latent posterior with an encoder and reconstructs through a decoder. This guide connects those ideas while directing each mechanism to its own lesson.
Assignment 3 in CS231N Spring 2026 is worth 15% of the grade and turns L8, L12–L14 and L16 into four Colab notebooks. Q1 has you write multi-head attention and a Transformer decoder for COCO captioning, then assemble a ViT and train it on CIFAR-10. Q2 implements SimCLR's augmentations and contrastive loss and compares linear classification with and without self-supervised pretraining. Q3 builds DDPM's noising, UNet, denoising loss, sampling and classifier-free guidance to generate text-conditioned 32×32 emoji. Q4 uses pretrained CLIP for similarity, zero-shot classification and retrieval, then segments a video with DINO features trained on a single labeled frame. This guide covers structure, files and targets only. No solutions.
The CS231N Spring 2026 diffusion lecture doesn't start with DDPM math. It opens by warning that terminology and notation in this area are a mess, then teaches one clean modern version: rectified flow. In training, pick a point between a data sample and noise and have the network predict the velocity from data toward noise; to generate, start from noise and walk backward for about 50 steps. The lecture then stacks on the practical pieces: classifier-free guidance, noise schedules that emphasize middle noise levels, diffusion on VAE latents, Transformers (DiT) as the denoiser, and distillation to cut the step count. Only at the end does it fold VP, VE, and ε/v-prediction into a generalized diffusion framework and name three mathematical views: latent variable model, score function, and SDE.
MIT 6.S184 is a short IAP (January Independent Activities Period) course: five lectures (Lecture 3 is split into two recordings, 3-A and 3-B), three labs, and an 84-page set of lecture notes the course calls its backbone. Notes, slides, all six recordings, lab notebooks, and official solutions are public, so it grades A3, enough to self-study. Two gaps remain: lab submission goes through Gradescope inside Canvas, which only enrolled MIT students can use, and Lecture 5 on discrete diffusion has no lab.
MIT 6.S184 Lab 1 has three parts. First you write the step functions for Euler and Euler–Maruyama. Then you use them to simulate Brownian motion and the Ornstein–Uhlenbeck process and watch how σ and θ shape trajectories and the final distribution. Finally you implement Langevin dynamics, watch a cloud of points get pushed toward a five-mode Gaussian mixture, and show by hand that the OU process is Langevin dynamics with a Gaussian target. The questions, code scaffolding, and official solutions are all on GitHub; outside readers get no Gradescope grading and have to check against the solutions themselves.
Lab 3 builds a conditional latent diffusion model on MNIST from scratch, in four stages: CFG training with label dropout (checked on a three-component Gaussian mixture), a diffusion transformer built piece by piece (Fourier time embedding, patchify, multi-head attention, adaLN-Zero, depatchify), a VAE, and finally the DiT trained inside the VAE's latent space. Problems and official solutions are public; submission goes through Gradescope on Canvas, which only enrolled MIT students can use.
Lecture 1 of MIT 6.S184 first rewrites "generate an image of a dog" as "sample from the data distribution," then gives the machine that does the sampling: start from Gaussian noise and simulate an ODE along a neural-network vector field (a flow model), or add a little Brownian-motion noise at every step to get an SDE (a diffusion model). Each is simulated with the simplest numerical method available, Euler and Euler–Maruyama. How to train the vector field is left to Lecture 2.
The object we want is the marginal vector field: run an ODE along it and noise flows into data. The catch is that it requires an integral over the whole dataset, so we can't compute it. Flow matching regresses on the conditional vector field instead, the one that pushes noise toward a single data point, which has a closed form. Theorem 12 in the notes shows the two losses differ by a constant and share the same gradient. On the CondOT path, training reduces to one line: sample data z, noise ε, and time t, and have the network predict z − ε at the point tz + (1−t)ε.
A score function is the gradient of the log density; it points toward where probability rises fastest. On Gaussian paths, the score and last lecture's vector field are both linear in x and z, so each converts into the other (Proposition 1 in the notes): learn one and you have learned both. With the score in hand, you can add noise of any strength to the ODE and turn it into an SDE without changing the distribution at any time (Theorem 17). The score itself is learned with the same trick as flow matching, by regressing on the conditional score. On Gaussian paths, that amounts to predicting the noise that was added, which is the DDPM training objective.
Feeding the prompt to the network as an extra input should, in theory, sample from p_data(x|y), but in practice the images don't follow the prompt closely enough. Lecture 3B uses Bayes' rule to split the guided vector field into the unguided vector field plus a classifier gradient; scaling that classifier term by w is classifier guidance. Replacing the classifier with the difference between guided and unguided fields gives CFG, which needs no classifier: ũ = (1−w)·u(x|∅) + w·u(x|y). Training only requires swapping the label for a null label ∅ with probability η. The costs: two network calls per step, and for w>1 you are no longer sampling from the data distribution.
The algorithms are complete by Lecture 3B; Lecture 4 tackles two engineering problems that show up at scale. First, the network must take an image, a time t, and a prompt and output a vector field of the same size, so we use a U-Net or a diffusion transformer (DiT), embedding time with Fourier features and text with frozen CLIP/T5 encoders. Second, pixel space is too big, so we first train a VAE to compress images into a latent space, run flow matching there, and decode at the end. Stable Diffusion 3 and Meta Movie Gen Video both follow this recipe: flow matching in latent space, a DiT variant, and CFG.
Text is a sequence of discrete tokens. There is no direction to move in, so ODEs and SDEs do not exist. Lecture 5 carries the recipe from Lectures 1–4 over unchanged and swaps only the underlying stochastic process: vector fields become rate matrices, ODEs become continuous-time Markov chains (CTMCs), and the continuity equation becomes the Kolmogorov forward equation. With the factorized mixture path, the marginal rate matrix has exactly one unknown: the probability of each position's original token given the noisy sequence. Training a discrete diffusion model therefore reduces to per-position classification with a cross-entropy loss. Make the noise all [mask] tokens and you get a masked diffusion language model.
L10 starts from one question: how do you find a good feature vector? Word2Vec learns embeddings through a pretext task. An autoencoder squeezes out a latent vector by being forced to reproduce its input. A VAE then asks the latent to follow a normal distribution, so nearby points produce similar images. Yen-Lung Tsai then recasts diffusion as "an autoencoder whose encoder is computed and whose decoder is learned", and ends on latent diffusion: a VAE shrinks a 512×512 image to 64×64, and diffusion runs only in that small space. The week 10 homework involves no code: make several style-consistent image sets with Bing.
L11 fills in the rest of the Stable Diffusion diagram. CLIP is trained so that matching text and images get similar vectors, which turns a prompt into a 77×768 embedding. Schedulers compress 1,000 noising steps into twenty or thirty denoising steps, but ancestral samplers such as Euler a never settle: push to 100 steps and the subject changes jackets and seats. LoRA freezes the original W and learns only a ΔW factored into A·B. The hands-on part loads an SD 1.5-family model with diffusers, and the week 11 homework is your own image-generation web app.
The Stable Diffusion setup from L11 listens only to the prompt, so composition and pose are left to luck. L12 adds a steering wheel. ControlNet copies a block of SD and wires the copy back in through zero convolutions, so extra conditions such as edge maps, poses, and depth maps can steer generation. The standard example is Canny edges. The second half covers Fooocus, an SD interface that aims to be 'as simple as Midjourney': Presets, Styles, and the five Input Image features, where Image Prompt is ControlNet with a friendly wrapper. Week 12 homework: pick a use case, make at least 3 image sets in Fooocus, and write up your creative process.
The last lecture looks at two lines of technology crossing into each other. LLMs such as ChatGPT have started drawing, and the slides use early fusion plus VQ-VAE/VQGAN to explain how an image can be cut into tokens. Going the other way, Inception Labs' Mercury generates text with diffusion, noising a sentence into a row of [MASK] tokens and then restoring it. Next come a few papers anyone can use: evaluating RAG automatically, reasoning models being easier to hijack, and DeepMind's four kinds of AI risk. The lecture ends with vibe coding and a list of application tools, and the final project runs as an online conference in Gather Town.
HW9 has 19 questions worth 10 points, answered only on NTU COOL with no code submission. The first 16 cover four papers — DDPM, Flow Matching, Rectified Flow, and MeanFlow — ending with questions that compare their training signals and few-step generation. The last 3 require the Colab: train two small MLPs on a 2D Swiss roll, one Flow Matching model that learns instantaneous velocity (always evaluated with 50 Euler steps, converged at Histogram JS ≤ 0.10) and one MeanFlow model that learns average velocity (always one-step, ≤ 0.40). Then compare 1 step vs 1 step, Flow Matching across Euler step counts, and Euler vs RK4 at equal steps and at similar compute. The PDF includes a generative-modeling tutorial that skips most of the math, and every question is published in Chinese and English. Outside readers miss only the COOL grading and answers.
The last CME295 lecture packs 128 slides into three parts: an eight-picture recap of the quarter, how Transformers handle images (ViT and two ways to build a VLM), and masked diffusion LLMs that emit several tokens per step, followed by what comes next in research and applications. It is not on the exam; the 2026 edition turns diffusion LLMs into a lecture of their own and refocuses Lecture 9 on multimodality.
The 2026 edition of CME295 gives diffusion LLMs a full lecture (Lecture 8, November 20), with five listed subtopics: continuous, discrete and masked diffusion, training, and inference. This pre-lecture edition works from the original papers (DDPM, D3PM, SEDD, MDLM, LLaDA and others): continuous noise costs about 64x the compute on text, and the [MASK] absorbing state won out; the training objective is a masked cross-entropy weighted by 1/t; the speed comes from filling several positions per step, yet LLaDA's main results decode one token per step, and Fast-dLLM needs a confidence threshold plus an approximate KV cache to reach up to a 27.6x speedup.
In Spring 2023, CS224U slipped two talks by members of its own teaching team into the Transformer unit. Lisa Li presented Diffusion-LM: instead of generating left to right one word at a time, it denoises a sequence of Gaussian vectors into word vectors. It loses to autoregressive models on both training and decoding efficiency, and in exchange lets a classifier's gradient steer the output at every step. Sidd Karamcheti showed how to cut GPT-2 Small's single-GPU training clock from 99.63 days to 3.37 days by stacking data parallelism, mixed precision, and ZeRO. The first talk survives only as slides; the second has slides and two recordings.
FLUX is Black Forest Labs' image-model family. The Stable Diffusion team launched it in August 2024 with a 12B rectified-flow transformer. Two years later it spans klein 4B ($0.014 and the only current Apache-2.0 model) / 9B, pro ($0.03), flex ($0.05), max ($0.07 with live web grounding), and open-weight 32B dev. FLUX 3 extends Self-Flow to video, synchronized audio, and robot actions. This guide covers the FLUX.1-to-FLUX 3 evolution, three-tier licensing, and model selection.
2021 was the year diffusion models surpassed GANs, self-supervised learning made theoretical breakthroughs, and reinforcement learning confronted weaknesses in its evaluation methodology. NeurIPS received a then-record 9,122 submissions, ICLR’s Score-Based Generative Modeling paper became a theoretical foundation for the diffusion ecosystem, and ICML delivered substantial work on optimization theory and the dynamics of self-supervised learning.
2021 was a dividing line for major AI conferences. Transformers spread from NLP throughout computer vision and time-series research, self-supervised learning became the most common cross-conference theme, and a diffusion model won an ICLR Outstanding Paper award before anyone realized it would displace GANs. Meanwhile, GNNs and federated learning reached historic peaks in paper volume before beginning to decline.
2022 was the year diffusion models took center stage, Chinchilla scaling laws rewrote large-model training, and Chain-of-Thought turned reasoning into an ability that prompts could elicit. NeurIPS passed 10,000 submissions; three of its 13 Outstanding Papers directly concerned diffusion; and Chinchilla and data pruning both challenged the belief that bigger was always better. On the eve of ChatGPT’s release, every required piece fell into place at that year’s conferences.
2022 was a turning point at major AI conferences. Diffusion models moved from emerging to mainstream, with two NeurIPS Outstanding Papers; Chinchilla rewrote scaling laws; Chain-of-Thought showed that large models could reason; and InstructGPT used RLHF to teach language models to follow instructions. When ChatGPT launched at year-end, these academic topics instantly became global news.
ML conference submissions exploded in 2024: NeurIPS received a record 15,671 papers, while ICML and ICLR passed 9,000 and 7,000. Research shifted from training ever-larger models toward spending inference compute more intelligently, making test-time compute scaling the year's defining new direction. VAR beat diffusion with next-scale image prediction, Rectified Flow became the theoretical foundation for Stable Diffusion 3, and ICLR gave its inaugural Test of Time Award to the original VAE paper.
The two strongest signals at AI conferences in 2025 were reasoning papers jumping from 47 to 216, a 4.6-fold rise, and agent-related terms exceeding 150 papers with 4.3–11-fold growth. Diffusion moved from breakout topic to infrastructure; RAG became a mainstream enterprise architecture with unusual coverage across all five conferences; state-space models and world models began tracing the early 2020–2021 path of Vision Transformers. Pure prompt-engineering papers encountered reviewer fatigue.