Flow Matching Dec 1, 2024

import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim

class FlowMatchingModel:
    def __init__(self, input_dim, hidden_dim):
        """
        Initialize Flow Matching Model
        
        Args:
            input_dim (int): Dimension of input data
            hidden_dim (int): Dimension of hidden layers
        """
        self.base_distribution = None  # Initial data distribution
        self.target_distribution = None  # Target data distribution
        
        # Neural network to learn the flow
        self.flow_network = nn.Sequential(
            nn.Linear(input_dim + 1, hidden_dim),  # +1 for time conditioning
            nn.ReLU(),
            nn.Linear(hidden_dim, hidden_dim),
            nn.ReLU(),
            nn.Linear(hidden_dim, input_dim)
        )
        
        self.optimizer = optim.Adam(self.flow_network.parameters())
    
    def sample_base_distribution(self, num_samples):
        """
        Sample from the base (initial) distribution
        
        Args:
            num_samples (int): Number of samples to generate
        
        Returns:
            torch.Tensor: Samples from base distribution
        """
        # Example: Gaussian distribution
        return torch.randn(num_samples, self.input_dim)
    
    def probability_flow_ode(self, x, t):
        """
        Compute the probability flow ODE
        
        Args:
            x (torch.Tensor): Current data point
            t (torch.Tensor): Time variable
        
        Returns:
            torch.Tensor: Flow direction
        """
        # Combine input and time as network input
        network_input = torch.cat([x, t], dim=1)
        return self.flow_network(network_input)
    
    def conditional_vector_field(self, x0, x1, t):
        """
        Compute the conditional vector field
        
        Args:
            x0 (torch.Tensor): Initial data point
            x1 (torch.Tensor): Target data point
            t (torch.Tensor): Time variable
        
        Returns:
            torch.Tensor: Conditional vector field
        """
        # Interpolate between source and target
        x_t = x0 * (1 - t) + x1 * t
        vector_field = x1 - x0
        return vector_field
    
    def loss_function(self, x0, x1):
        """
        Compute the flow matching loss
        
        Args:
            x0 (torch.Tensor): Initial data points
            x1 (torch.Tensor): Target data points
        
        Returns:
            torch.Tensor: Training loss
        """
        batch_size = x0.shape[0]
        t = torch.rand(batch_size, 1)  # Random time sampling
        
        # Compute vector field
        true_vector_field = self.conditional_vector_field(x0, x1, t)
        predicted_vector_field = self.probability_flow_ode(x0, t)
        
        # Compute MSE loss between true and predicted vector fields
        loss = torch.mean((predicted_vector_field - true_vector_field) ** 2)
        return loss
    
    def train(self, dataloader, epochs):
        """
        Train the Flow Matching Model
        
        Args:
            dataloader (torch.utils.data.DataLoader): Training data
            epochs (int): Number of training epochs
        """
        for epoch in range(epochs):
            for batch_x0, batch_x1 in dataloader:
                self.optimizer.zero_grad()
                loss = self.loss_function(batch_x0, batch_x1)
                loss.backward()
                self.optimizer.step()
            
            print(f"Epoch {epoch+1}/{epochs}, Loss: {loss.item()}")
    
    def generate_samples(self, num_samples):
        """
        Generate new samples using the learned flow
        
        Args:
            num_samples (int): Number of samples to generate
        
        Returns:
            torch.Tensor: Generated samples
        """
        # Start from base distribution and follow the learned flow
        x0 = self.sample_base_distribution(num_samples)
        
        # Perform sampling through ODE solving
        x_generated = x0  # Starting point
        time_steps = torch.linspace(0, 1, 100)
        
        for t in time_steps[1:]:
            vector_field = self.probability_flow_ode(x_generated, t)
            x_generated += vector_field * (time_steps[1] - time_steps[0])
        
        return x_generated

def main():
    # Hyperparameters
    input_dim = 10
    hidden_dim = 64
    num_epochs = 100
    
    flow_matching = FlowMatchingModel(input_dim, hidden_dim)
    flow_matching.train(dataloader, num_epochs)
    generated_samples = flow_matching.generate_samples(1000)