CS 9840: Probabilistic Generative AI
Summarized course website for CS 9840: Probabilistic GenAI, Winter 2026. Students will learn the theoretical foundations for generative AI.
From chatbots to image generators, Generative AI (GenAI) is reshaping the world. What algorithms and probabilistic principles power this revolution? This course introduces the theoretical and algorithmic foundations of GenAI, covering large language models (LLMs) and diffusion models, among more mature methods. We will also explore applications in AI for Science, such as drug discovery and weather forecasting.
Detailed course information is on OWL Brightspace (available starting Jan 2026) and the course outline.
Prerequisites
There are no formal prerequisites. But, since GenAI is inherently probabilistic, some knowledge of the following is necessary.
There will be review sessions (Weeks 1 & 2). However, students who are not comfortable with these concepts are highly encouraged to independently read the D2L book, Chapter 2.
- Probability/statistics:
- sum, product, and Bayes' rule,
- probability distributions (Gaussians, Categorical),
- maximum likelihood.
- Linear algebra:
- vectors and matrices,
- matrices/vectors products,
- matrix inversion.
- Multivariable calculus:
- partial derivatives, gradients, Jacobians, & Hessians,
- multivariable integration.
- Machine learning:
- regression, classification,
- neural networks,
- gradient descent,
- familiarity with deep learning libraries (code examples are in PyTorch).
Schedule
- Lecture: Tuesdays, 10 AM–12 PM.
- Tutorial: Thursdays, 1:00 PM–2:00 PM.
- Office hour: Thursdays, 2:00 PM–3:00 PM.
| Week | Date | Lecture (Tue) | Tutorial (Thu) | Resources |
|---|---|---|---|---|
| 1 | Jan 6 | Introduction, probability review, admins | Linear algebra & calculus review | Bishop 2024, Chapters 2 & 3; D2L, Chapter 2 |
| 2 | Jan 13 | Neural networks review & deterministic autoencoders | Variational autoencoders | Bishop 2024, Chapter 19; D2L, Chapter 2 |
| 3 | Jan 20 | Explicit and implicit likelihood models | Project info session | Bishop 2024, Chapters 17 & 18 |
| 4 | Jan 27 | Application: Latent space Bayesian optimization | Selected topics in GenAI | Kristiadi 2025, Chapter 1; Garnett 2023, Chapter 1; Gómez-Bombarelli et al., ACS 2018 |
| 5 | Feb 3 | Diffusion Models I: Introduction | Stylistic scientific writing 101 | Bishop 2024, Chapter 20 |
| 6 | Feb 10 | Diffusion Models II: Advanced Topics | HW 1 | Bishop 2024, Chapter 20 |
| 7 | Feb 17 | Reading week | No classes | |
| 8 | Feb 24 | Application: Climate modeling | Project proposal deadline & HW 2 | Price et al., Nature 2025 |
| 9 | Mar 3 | LLMs I: Architectures | HW 3 | Bishop 2024, Chapter 12; D2L Chapter 11 |
| 10 | Mar 10 | LLMs II: Decoding and reasoning | HW 4 | Bishop 2024, Sec. 12.3.2; D2L Sec. 10.8; Lightman et al., ICLR 2023 |
| 11 | Mar 17 | LLMs III: Finetuning and alignment | Q&A, any topics. Submit questions in advance on Slido. | Bishop 2024, Chapter 12; Steinnon et al., NeurIPS 2020; Hu et al., ICLR 2022 |
| 12 | Mar 24 | Uncertainty quantification in GenAI | Q&A, any topics. Submit questions in advance on Slido. | Kendall and Gal, NIPS 2017 |
| 13 | Mar 31 | Project presentations | Project presentations |
- HW 1–4 due at 12 PM (noon) on the day of the respective tutorial.
- Project proposal must be submitted by Thursday, Feb 26, 12 PM (noon).
- Project presentation slides must be submitted by Monday, Mar 30, 11:59 PM. The presentation order will be drawn randomly.
- Project final report must be submitted by Thursday, Apr 9, 11:59 PM.
References
- Bishop, "Deep Learning: Foundations and Concepts", Springer, 2024. [Link]
- Zhang, Lipton, Li, and Smola, "Dive into Deep Learning (D2L)". [Link]
- Garnett, Roman, "Bayesian Optimization", Cambridge University Press, 2023. [Link]
- Kristiadi, Agustinus, "Introduction to the Analysis of Probabilistic Decision-Making Algorithms", 2025. [Link]
- Gómez-Bombarelli, et al., "Automatic chemical design using a data-driven continuous representation of molecules", ACS Central Science 4(2), 2018. [Link]
- Price, et al., "Probabilistic weather forecasting with machine learning", Nature 637(8044), 2025. [Link]
- Stiennon, et al., "Learning to summarize with human feedback", NeurIPS, 2020. [Link]
- Lightman, et al., "Let's verify step by step." ICLR. 2023. [Link]
- Hu, et al., "LoRA: Low-rank adaptation of large language models", ICLR, 2022. [Link]
- Kendall and Gal. "What uncertainties do we need in Bayesian deep learning for computer vision?", NIPS, 2017. [Link]
Grading
Students will be asked to form groups of 2 in the early weeks of the course. All homeworks and project are to be done in group. Homework assignment sheets will be available on OWL Brightspace. Refer to the course outline for detailed information.
| Type | Weight | Count | Total |
|---|---|---|---|
| Homework | 10% | 4 | 40% |
| Project Proposal | 15% | 1 | 15% |
| Project Final Presentation | 20% | 1 | 20% |
| Project Final Report | 25% | 1 | 25% |
| Total | - | - | 100% |
Policies
- GenAI such as LLM chatbots must not be used to generate HW solutions and reports/slides.
- Acceptable use of GenAI: (Must be disclosed as at the end of each document.)
- Grammar correction.
- "Study Mode": https://openai.com/index/chatgpt-study-mode/.
- Late submissions will not be marked since HWs and project are done in a group.
Refer to the course outline for more info and other polices.