In this section, I implemented a UNet architecture for single-step denoising. The model was trained to map noisy MNIST digits back to their clean versions using an L2 loss function. The UNet consists of downsampling and upsampling blocks with skip connections.

1.2 Training Process

The training process involved generating noisy versions of MNIST digits using various sigma values. Below shows the effect of different noise levels on the input images:

Figure 3: Varying levels of noise on MNIST digits

Training Results

Figure 4: Training Loss Curve over 5 Epochs

Figure 5: Results on test set after 1 epoch of training

Figure 6: Results on test set after 5 epochs of training

1.2.2 Out-of-Distribution Testing

To evaluate the model's generalization capabilities, we tested it on noise levels (σ) that weren't seen during training. The results below show how the model performs across different noise intensities:

σ = 0.0

σ = 0.2

σ = 0.4

σ = 0.5

σ = 0.6

σ = 0.8

σ = 1.0

You can see that lower noise levels result in more accurate denoising, while higher noise levels result in more blurry images and more error.

In this section, I implemented a time-conditioned UNet for diffusion modeling. The model was trained to predict noise at different timesteps, enabling iterative denoising of images. This builds upon the basic UNet from Part B1 by adding time conditioning through FCBlocks.

Architecture Modifications

The UNet architecture was modified to include time conditioning through FCBlocks:

• Added two FCBlocks for time embedding
• Modified the unflatten and up1 layers to incorporate time information
• Normalized time values to [0,1] range before embedding

Training Process

The model was trained with the following specifications:

• Batch size: 128
• Hidden dimension: 64
• Learning rate: 1e-3 with exponential decay
• Training duration: 20 epochs

Training Loss Over 20 Epochs

Sampling Results

Below are the sampling results after 5 and 20 epochs of training. The model shows improvement in generation quality as training progresses.

Generated Samples after 5 Epochs

Generated Samples after 20 Epochs

Analysis

The training loss curve shows steady improvement over the 20 epochs, with the most significant improvements occurring in the first 10 epochs. The sampling results demonstrate the model's ability to generate increasingly clear and coherent MNIST digits as training progresses.

Building upon the time-conditioned UNet, this section implements additional class conditioning to enable controlled generation of specific MNIST digits. The model now accepts both time step t and class label c as conditioning signals.

Architecture Enhancements

The UNet architecture was further modified to include class conditioning:

• Added two additional FCBlocks for class embedding
• Implemented one-hot encoding for class labels (0-9)
• Added class conditioning dropout (p=0.1) for unconditional training
• Modified the modulation scheme to incorporate both time and class information

Training Configuration

The model was trained with the following specifications:

• Batch size: 128
• Hidden dimension: 64
• Learning rate: 1e-3 with exponential decay
• Training duration: 20 epochs
• Class conditioning dropout: 10%
• Classifier-free guidance scale: 5.0

Training Loss Over 20 Epochs

Generation Results

Below are the sampling results after 5 and 20 epochs of training, showing four instances of each digit (0-9). The results demonstrate the model's ability to generate specific digits while maintaining variation within each class.

Generated Samples after 5 Epochs (4 instances per digit)

Generated Samples after 20 Epochs (4 instances per digit)

Analysis

The class-conditioned model shows several improvements over the time-only conditioned version and improved with higher epochs.