Algorithm Overview - Flow Matching is a generative model that aims to generate samples similar to a given target set without any input [3][4] - The model learns a direction of movement from a source point to a target point, effectively generating new samples by iteratively adjusting the position towards the target [14][17] Training and Inference - During training, the model samples points along the line connecting source and target, learning the average slope from multiple connections [16][17] - In inference, the model starts from a noise point and moves towards the target, gradually collapsing to a specific state as it approaches the target [17][18] Code Implementation - The implementation involves generating random inputs, predicting the slope using a neural network, and applying an optimization process to minimize the loss between predicted and target slopes [18][19] - The code includes hyperparameters for dimensions, sample sizes, and training epochs, demonstrating a straightforward approach to implementing the Flow Matching algorithm [19][25] Advanced Applications - The model can be adapted to generate samples based on prompts, allowing for more controlled generation by segmenting the target distribution [24][29] - A more complex example includes generating handwritten digits from the MNIST dataset, showcasing the model's versatility in handling different types of data [30][32] Model Architecture - The architecture includes a UNet backbone for predicting the velocity field, which enhances performance through multi-scale feature fusion [32][34] - The model incorporates conditional inputs to refine the generation process, ensuring that the output aligns with specified conditions [34][35] Training Process - The training loop involves generating dynamic noise, calculating the loss based on the difference between predicted and actual images, and updating the model parameters accordingly [40][41] - The model is designed to visualize generated samples periodically, providing insights into its performance and output quality [40][41]