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 December 2025) 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 @ MC 320.
- Tutorial: Thursdays, 12:30 PM–1:30 PM @ MC 320.
- Office hour: Thursdays, 1:30 PM–3:00 PM @ MC 362.
| Week | Date | Lecture (Tue) | Tutorial (Thu) | Resources |
|---|---|---|---|---|
| 1 | Jan 6 | Introduction & review of fundamentals | Review of fundamentals | Bishop 2024, Chapters 2 & 3; D2L, Chapter 2 |
| 2 | Jan 13 | Variational autoencoders | Review of fundamentals | Bishop 2024, Chapter 19; D2L, Chapter 2 |
| 3 | Jan 20 | Explicit and implicit models | HW 1 | Bishop 2024, Chapters 17 & 18 |
| 4 | Jan 27 | Application: De novo drug discovery | HW 2 | Gómez-Bombarelli, et al., 2018 |
| 5 | Feb 3 | Diffusion Models I: Introduction | Project info session | Bishop 2024, Chapter 20 |
| 6 | Feb 10 | Diffusion Models II: Advanced Topics | Project proposal deadline & project Q&A | Bishop 2024, Chapter 20 |
| 7 | Feb 17 | Reading week | No classes | |
| 8 | Feb 24 | Application: Climate modeling | HW 3 | |
| 9 | Mar 3 | LLMs I: Architectures | Stylistic scientific writing 101 | 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., 2023 |
| 11 | Mar 17 | LLMs III: Finetuning and alignment | Selected topics in GenAI | Bishop 2024, Chapter 12; Steinnon et al, NeurIPS 2020; Hu et al., ICLR 2022 |
| 12 | Mar 24 | Project presentations | Project presentations | |
| 13 | Mar 31 | Project presentations | Project presentations |
- HW 1-4 must be submitted the midnight before the corresponding tutorial. For example, HW 1 must be submitted by Wednesday, Jan 21, 11:59 PM.
- Project proposal must be submitted by Wednesday, Feb 12, 11:59 PM.
- Project presentation slides must be submitted by Monday, Mar 23, 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]
- 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]
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.