---
title: Diffusion Models - Complete DDPM Implementation
emoji: 🌊
colorFrom: purple
colorTo: pink
sdk: pytorch
app_file: "Diffusion Models.ipynb"
pinned: false
license: mit
tags:
- deep-learning
- generative-ai
- pytorch
- diffusion-models
- ddpm
- denoising
- generative-modeling
- computer-vision
- unsupervised-learning
datasets:
- synthetic-2d-data
---

# Diffusion Models: Complete DDPM Implementation

A comprehensive PyTorch implementation of Denoising Diffusion Probabilistic Models (DDPM) with detailed mathematical foundations and educational content.

## Model Description

This repository contains a complete implementation of Diffusion Models (DDPM) trained on 2D synthetic datasets. The model learns to generate new data points by mastering the art of noise removal through a reverse diffusion process. This implementation serves as both a working model and an educational resource for understanding the mathematics and implementation of diffusion models.

### Architecture Details

- **Model Type**: Denoising Diffusion Probabilistic Model (DDPM)
- **Framework**: PyTorch
- **Input**: 2D point coordinates
- **Diffusion Steps**: 1000 timesteps
- **Hidden Dimensions**: 256 units with SiLU activations
- **Time Embedding**: 64-dimensional rich representations
- **Total Parameters**: ~130K
- **Model Size**: 1.8MB

### Key Components

1. **Noise Predictor Network**: Neural network that predicts noise ε_θ(x_t, t)
2. **Forward Diffusion Process**: Gradually adds Gaussian noise over T steps
3. **Reverse Diffusion Process**: Iteratively removes noise to generate samples
4. **Time Embedding Module**: Converts timesteps to rich feature representations

## Training Details

- **Dataset**: Synthetic 2D point clusters
- **Diffusion Steps**: 1000
- **Beta Schedule**: Linear (0.0001 to 0.02)
- **Optimizer**: AdamW with cosine annealing
- **Learning Rate**: 0.001
- **Training Epochs**: 2000
- **Batch Processing**: Dynamic batching for efficient training

## Mathematical Foundation

### Forward Process
The forward process adds noise according to:
```
q(x_t | x_{t-1}) = N(x_t; √(1-β_t) x_{t-1}, β_t I)
```

With direct sampling:
```
x_t = √ᾱ_t x_0 + √(1-ᾱ_t) ε
```

### Reverse Process
The model learns to reverse noise:
```
p_θ(x_{t-1} | x_t) = N(x_{t-1}; μ_θ(x_t, t), Σ_θ(x_t, t))
```

### Loss Function
Trained by minimizing noise prediction error:
```
L = E[||ε - ε_θ(x_t, t)||²]
```

## Model Performance

### Training Metrics
- **Final Training Loss**: Converged to stable low values
- **Training Time**: ~30 minutes on GPU
- **Memory Usage**: <500MB GPU memory
- **Convergence**: Stable training without mode collapse

### Capabilities
- ✅ High-quality 2D point generation
- ✅ Smooth interpolation in data space
- ✅ Stable training without adversarial dynamics
- ✅ Mathematically grounded approach
- ✅ Excellent sample diversity

## Usage

### Quick Start

```python
import torch
import torch.nn as nn
import matplotlib.pyplot as plt

# Load the model components (full implementation in notebook)
class NoisePredictor(nn.Module):
    def __init__(self, data_dim=2, hidden_dim=256, time_embed_dim=64):
        super(NoisePredictor, self).__init__()
        # ... (complete implementation in notebook)
    
    def forward(self, x, t):
        # ... (complete implementation in notebook)
        return noise_prediction

class DiffusionModel:
    def __init__(self, T=1000, beta_start=0.0001, beta_end=0.02):
        # ... (complete implementation in notebook)
    
    def sample(self, n_samples=100):
        # Generate new samples from pure noise
        # ... (complete implementation in notebook)
        return generated_samples

# Load trained model
model = DiffusionModel()
# Load weights: model.model.load_state_dict(torch.load('diffusion_model_complete.pth'))

# Generate new samples
samples = model.sample(n_samples=100)
plt.scatter(samples[:, 0], samples[:, 1])
plt.title("Generated 2D Points")
plt.show()
```

### Advanced Usage

```python
# Visualize the diffusion process
model.visualize_diffusion_process()

# Monitor training progress
model.plot_training_curves()

# Sample with different parameters
high_quality_samples = model.sample(n_samples=500, guidance_scale=1.0)
```

## Visualizations Available

1. **Diffusion Process**: Step-by-step noise addition and removal
2. **Training Curves**: Loss evolution and learning dynamics
3. **Generated Samples**: Comparison with original data distribution
4. **Sampling Process**: Real-time generation visualization
5. **Parameter Analysis**: Beta schedule and noise analysis

## Files and Outputs

- `Diffusion Models.ipynb`: Complete implementation with educational content
- `diffusion_model_complete.pth`: Trained model weights
- `diffusion_process.png`: Visualization of forward and reverse processes
- `diffusion_results.png`: Generated samples and quality assessment
- `training_metrics.png`: Comprehensive training analytics
- `diffusion_logs/`: Detailed training and sampling logs

## Applications

This diffusion model implementation can be adapted for:

- **Image Generation**: Extend to pixel-based image synthesis
- **Audio Synthesis**: Apply to waveform or spectrogram generation
- **3D Point Clouds**: Generate 3D shapes and objects
- **Time Series**: Financial data, sensor readings, weather patterns
- **Scientific Data**: Molecular structures, particle physics
- **Data Augmentation**: Synthetic training data creation

## Educational Value

This implementation is designed as a learning resource featuring:

- **Complete Mathematical Derivations**: From first principles to implementation
- **Step-by-Step Explanations**: Every component explained in detail
- **Visual Learning**: Rich plots and animations for understanding
- **Progressive Complexity**: Build understanding gradually
- **Practical Implementation**: Real working code with best practices

## Research Applications

The model demonstrates key concepts in:

- **Generative Modeling**: Alternative to GANs and VAEs
- **Probability Theory**: Markov chains and stochastic processes
- **Neural Network Architecture**: Time conditioning and embeddings
- **Optimization**: Stable training of generative models
- **Sampling Methods**: DDPM and potential DDIM extensions

## Comparison with Other Generative Models

### Advantages over GANs
- ✅ Stable training (no adversarial dynamics)
- ✅ No mode collapse
- ✅ Mathematical foundation
- ✅ High-quality samples

### Advantages over VAEs
- ✅ Higher sample quality
- ✅ No posterior collapse
- ✅ Better likelihood estimates
- ✅ Flexible architectures

### Trade-offs
- ⚠️ Slower sampling (requires multiple steps)
- ⚠️ More computationally intensive
- ⚠️ Memory requirements for long sequences

## Citation

If you use this implementation in your research or projects, please cite:

```bibtex
@misc{ddpm_implementation_2024,
  title={Complete DDPM Implementation: Educational Diffusion Models},
  author={Gruhesh Kurra},
  year={2024},
  url={https://huggingface.co/karthik-2905/DiffusionModels}
}
```

## Future Extensions

Planned improvements and extensions:

- 🔄 **DDIM Implementation**: Faster sampling with deterministic steps
- 🎨 **Conditional Generation**: Text-guided or class-conditional generation
- 📊 **Alternative Schedules**: Cosine and sigmoid beta schedules
- 🖼️ **Image Diffusion**: Extension to CIFAR-10 and other image datasets
- 🎵 **Audio Applications**: Waveform and spectrogram generation
- 🧬 **Scientific Applications**: Molecular and protein structure generation

## License

This project is licensed under the MIT License - see the LICENSE file for details.

## Additional Resources

- **GitHub Repository**: [DiffusionModels](https://github.com/GruheshKurra/DiffusionModels)
- **Detailed Notebook**: Complete implementation with educational content
- **Training Logs**: Comprehensive metrics and analysis

## Model Card Authors

**Gruhesh Kurra** - Implementation, documentation, and educational content

---

**Tags**: diffusion-models, generative-ai, pytorch, ddpm, deep-learning, denoising

**Model Card Last Updated**: December 2024