--- 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