# 6.8300 Problem Set #5: Representation Learning and Diffusion Models

In this problem set, we will
1. compare different strategies for representation learning and
2. do a deep-dive into diffusion models.

Note that much of this problem set requires GPUs.
- Feel free to use your own GPU(s) if you have access. If so, you'll need to install the requirements in `requirements.txt` in each of `part1` and `part2`.
- To work on this problem set using GPUs in Google Colab, copy the `pset-5` directory to your Google Drive. When working on a particular notebook, configure the notebook to use a GPU machine with `Runtime → Change runtime type → T4 GPU`.

**IMPORTANT**: Resources on Google Colab are limited! If you use the GPUs for too long (e.g., several hours), they may restrict your GPU access for a while. To avoid issues, please start this assignment early and close the notebook when you're not actively using it.

## Part 1: Representation Learning

In the first part, we'll compare representations from two different representation learning methods.
For this part, we'll be working in `part1/representations.ipynb`.
To get started, open this notebook in Google Colab and follow the instructions there.

### Submission Guidelines for Part 1

The only deliverable for this problem is `part1/representations.py`.
Please submit this file to Gradescope.

## Part 2: Diffusion Models

In this part, we will be working in the four ipynb files in `part2/`, corresponding to each problem. Please submit an aggregated PDF file with answers to and figures generated in **_all_** problems, along with the four notebooks with your code and running outputs.

### Submission Guidelines for Part 2

Please include your answer to all problems, including formulas, proofs, and the figures generated in each problem, excluding code. You are required to submit the (single) PDF titled `part2.pdf` and all (four) notebooks with your code and running outputs. Do not include code in the PDF file. 

Specifically, the PDF should contain:
- Problem 1
  - Formulas and proofs for problem 1.1 and 1.2
  - 4 figures, one for each beta schedule for problem 1.3
  - Answers to the 2 short answer questions about different beta schedules in problem 1.3
- Problem 2
  - The generated figures `results/p2_train_plot.png` and `results/p2_toy_samples.png`
- Problem 3
  - The generated figures `results/mnist_train_plot.png` and `results/image_w{w}.png` (w=0.0, 0.5, 1.0, 2.0, 4.0)
  - Answer to the short answer question about the U-Net architecture
  - Answer to the short answer question about different CFG weight $w$ in problem 3.2
- Problem 4
  - The generated figures `results/sampling_comparison.png`
  - Answer to the short answer question about different samplers and number of steps

## Grading

Part 1: Representation learning
 - 20 points

Part 2: Diffusion models
 - Problem 1: 15 points
 - Problem 2: 30 points
 - Problem 3: 20 points
 - Problem 4: 15 points

### Acknowledgements

Parts of this pset were inspired by
* Berkeley CS294-158, taught by Pieter Abbeel, Wilson Yan, Kevin Frans, and Philipp Wu;
* MIT 6.S184/6.S975, taught by Peter Holderrieth and Ezra Erives;
* The [blog post](https://lilianweng.github.io/posts/2021-07-11-diffusion-models/) about diffusion models by Lilian Weng.