In this project, you will work with Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs). You will build and train conditional versions of these models to generate MNIST digits given a digit class (see also Labels improve subjective sample quality, in week 12).

Objectives

1. Conditional Variational Autoencoder (C-VAE): Implement a Conditional VAE that takes an MNIST image and its associated label as input. The model should learn to generate new images that resemble the input image given a class label.
2. Conditional Generative Adversarial Network (C-GAN): Implement a Conditional GAN that takes a random noise vector and a class label as input to the generator, and produces a digit of the specified class. The discriminator should also be conditioned on the class label.
3. Model Comparison: Compare the performance of the two models. Discuss their strengths and weaknesses, and compare the quality of the generated samples. Use both qualitative (visual) and quantitative measures (if possible) for this comparison.
4. Extra Challenge (Optional): Experiment with different architectures, training strate- gies, and techniques for improving the quality and diversity of the generated images (such as different types of regularisation, different architectures, etc.). Document your findings and provide explanations for the observed results.

Deliverables

1. Code: Well-commented Python scripts or Jupyter notebooks for both the C-VAE and C- GAN implementations. The code should include data loading, model definition, training loop, and a testing routine to generate new samples given class labels.
2. Report: A brief report that includes the following:
   1. Model descriptions: An overview of the implemented models, including the chosen ar- chitectures and specific implementation details. Provide references to external sources and texts.
   1. Training details: Information about the training process, such as loss curves, training times, and any issues encountered.
   1. Results: Include generated samples from both models, and any quantitative results if computed.
   • Discussion: A comparison of the models, any insights gained from the project, and suggestions for future work or improvements.

The key goal of this project is not only to implement the models, but to gain a deeper understand- ing of VAEs and GANs, how conditioning on labels affects their performance, and the trade-offs between the two models.