# DDPM — Fashion-MNIST

A simple DDPM implementation built from scratch using PyTorch.

The model learns to predict the noise added to a real Fashion-MNIST image.

## Pipeline

Training:

    x₀ → add noise → xₜ → U-Net → predicted noise
                              ↓
                         MSE Loss

Sampling:

    Gaussian Noise
          ↓
        U-Net
          ↓
      Denoising
          ↓
        U-Net
          ↓
         ...
          ↓
     Generated Image

## Model

The U-Net takes:

    (xₜ, t)

and predicts:

    εθ(xₜ, t)

The U-Net contains:

- Time embedding
- Input convolution
- 2 downsampling blocks
- 2 middle ResBlocks
- 2 upsampling blocks
- Skip connections
- GroupNorm
- SiLU activation
- Final output convolution

Input:

    [B, 1, 28, 28]

Output:

    [B, 1, 28, 28]

The output represents predicted Gaussian noise.

## Forward Diffusion

We use:

    xₜ = √ᾱₜ x₀ + √(1 - ᾱₜ) ε

where:

    ε ~ N(0, I)

## Training

For every batch:

1. Take a real image x₀.
2. Select a random timestep t.
3. Generate Gaussian noise ε.
4. Create xₜ using the forward diffusion process.
5. Give xₜ and t to the U-Net.
6. Predict the noise.
7. Calculate MSE between predicted and actual noise.
8. Update the U-Net.

## Reverse Diffusion

During generation, we start from:

    xT ~ N(0, I)

and move backwards:

    xT → xT-1 → ... → x1 → x0

At every timestep, the U-Net predicts the noise and the DDPM scheduler performs one reverse step.

## Checkpoint

Model weights are saved using:

    .safetensors

Example:

    checkpoints/ddpm_fashion_mnist.safetensors

The model architecture must be recreated before loading the weights.

## Dataset

Dataset:

    Fashion-MNIST

Image size:

    28 × 28

Channels:

    1

## Goal

The goal of this project is to understand DDPM from first principles:

    Forward Diffusion
          ↓
       U-Net
          ↓
    Noise Prediction
          ↓
    Reverse Diffusion
          ↓
    Image Generation