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de2377a | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 | """
Flow Matching implementation for continuous normalizing flows.
Flow matching learns a velocity field v(x, t) that transports samples from a noise
distribution to the data distribution via ordinary differential equations (ODEs).
Reference: "Flow Matching for Generative Modeling" (Lipman et al., 2023)
"""
import torch
import torch.nn as nn
from tqdm import tqdm
class FlowMatching(nn.Module):
"""
Flow Matching model that learns to transport noise to data via velocity fields.
Args:
model: Neural network that predicts velocity field v(x, t)
Should take (x, t) and return predicted velocity of same shape as x
sigma: Standard deviation for conditional flow matching (default: 0.0)
When sigma > 0, uses conditional flow matching with Gaussian paths
"""
def __init__(self, model, sigma=0.0):
super().__init__()
self.model = model
self.sigma = sigma
def forward(self, x_0, return_loss=True):
"""
Compute flow matching loss for a batch of data.
Forward process:
- Sample t uniformly from [0, 1]
- Sample noise x_1 ~ N(0, I)
- Interpolate: x_t = t * x_0 + (1 - t) * x_1
- True velocity: v_t = x_0 - x_1
- Loss: MSE(predicted_velocity, true_velocity)
Args:
x_0: Clean data samples (B, D)
return_loss: If True, return scalar loss. If False, return per-sample losses
Returns:
loss: Scalar loss if return_loss=True, else (B,) tensor of per-sample losses
"""
batch_size = x_0.shape[0]
device = x_0.device
# Sample random timesteps uniformly from [0, 1]
t = torch.rand(batch_size, device=device)
# Sample noise from standard normal
x_1 = torch.randn_like(x_0)
# Interpolate between noise and data
# x_t = t * x_0 + (1 - t) * x_1
t_expanded = t.view(batch_size, *([1] * (x_0.ndim - 1))) # (B, 1, 1, ...)
x_t = t_expanded * x_0 + (1 - t_expanded) * x_1
# True velocity field: dx_t/dt = x_0 - x_1
# This is the derivative of the linear interpolation
true_velocity = x_0 - x_1
# Add Gaussian noise for conditional flow matching (if sigma > 0)
if self.sigma > 0:
x_t = x_t + self.sigma * torch.randn_like(x_t)
# Predict velocity using the model
predicted_velocity = self.model(x_t, t)
# Compute MSE loss
loss = (predicted_velocity - true_velocity) ** 2
if return_loss:
return loss.mean()
else:
# Return per-sample loss (averaged over dimensions)
return loss.view(batch_size, -1).mean(dim=1)
@torch.no_grad()
def sample(self,
sample_shape,
device='cuda',
num_steps=100,
method='euler',
return_intermediates=False,
save_interval=10,
verbose=True):
"""
Generate samples by solving the ODE: dx/dt = v(x, t) from t=0 to t=1.
Args:
sample_shape: Shape of samples to generate (B, D)
device: Device to generate samples on
num_steps: Number of integration steps (default: 100)
method: ODE solver method ('euler', 'midpoint', 'rk4')
return_intermediates: If True, return intermediate states
save_interval: Save intermediate states every N steps (if return_intermediates=True)
verbose: Show progress bar
Returns:
samples: Generated samples (B, D)
intermediates: List of (t, x_t) tuples (if return_intermediates=True)
"""
# Start from noise at t=0
x = torch.randn(sample_shape, device=device)
# Time steps from 0 to 1
timesteps = torch.linspace(0, 1, num_steps + 1, device=device)
dt = 1.0 / num_steps
intermediates = []
if return_intermediates:
intermediates.append((0.0, x.cpu().clone()))
# Progress bar
iterator = tqdm(range(num_steps), desc='Sampling') if verbose else range(num_steps)
for i in iterator:
t = timesteps[i]
# Create batch of timesteps
t_batch = torch.full((sample_shape[0],), t, device=device)
if method == 'euler':
# Euler method: x_{t+dt} = x_t + dt * v(x_t, t)
v = self.model(x, t_batch)
x = x + dt * v
elif method == 'midpoint':
# Midpoint method (RK2)
# k1 = v(x_t, t)
# k2 = v(x_t + 0.5*dt*k1, t + 0.5*dt)
# x_{t+dt} = x_t + dt * k2
k1 = self.model(x, t_batch)
t_mid = t + 0.5 * dt
t_mid_batch = torch.full((sample_shape[0],), t_mid, device=device)
k2 = self.model(x + 0.5 * dt * k1, t_mid_batch)
x = x + dt * k2
elif method == 'rk4':
# Classic RK4 method
t_half = t + 0.5 * dt
t_next = t + dt
t_batch_half = torch.full((sample_shape[0],), t_half, device=device)
t_batch_next = torch.full((sample_shape[0],), t_next, device=device)
k1 = self.model(x, t_batch)
k2 = self.model(x + 0.5 * dt * k1, t_batch_half)
k3 = self.model(x + 0.5 * dt * k2, t_batch_half)
k4 = self.model(x + dt * k3, t_batch_next)
x = x + (dt / 6.0) * (k1 + 2*k2 + 2*k3 + k4)
else:
raise ValueError(f"Unknown method: {method}. Choose from 'euler', 'midpoint', 'rk4'")
# Save intermediate states
if return_intermediates and (i + 1) % save_interval == 0:
intermediates.append((timesteps[i + 1].item(), x.cpu().clone()))
# Final state at t=1
if return_intermediates:
if len(intermediates) == 0 or intermediates[-1][0] != 1.0:
intermediates.append((1.0, x.cpu().clone()))
return x, intermediates
return x
@torch.no_grad()
def sample_ode(self,
sample_shape,
device='cuda',
rtol=1e-5,
atol=1e-5,
method='dopri5',
return_intermediates=False,
verbose=True):
"""
Generate samples using adaptive ODE solvers from torchdiffeq.
This method uses scipy-style adaptive solvers that automatically
adjust step sizes for accuracy. Requires: pip install torchdiffeq
Args:
sample_shape: Shape of samples to generate (B, D)
device: Device to generate samples on
rtol: Relative tolerance for ODE solver
atol: Absolute tolerance for ODE solver
method: Solver method ('dopri5', 'dopri8', 'adams', 'rk4', etc.)
return_intermediates: If True, return trajectory
verbose: Print status messages
Returns:
samples: Generated samples (B, D)
trajectory: Full trajectory if return_intermediates=True
"""
try:
from torchdiffeq import odeint
except ImportError:
raise ImportError(
"torchdiffeq is required for adaptive ODE solvers. "
"Install with: pip install torchdiffeq"
)
if verbose:
print(f"Sampling with adaptive ODE solver: {method}")
# Start from noise at t=0
x_0 = torch.randn(sample_shape, device=device)
# Define velocity field function
def velocity_fn(t, x):
# t is a scalar tensor, need to broadcast to batch
t_batch = torch.full((sample_shape[0],), t.item(), device=device)
return self.model(x, t_batch)
# Integration time points
if return_intermediates:
# Return full trajectory with 100 points
t_span = torch.linspace(0, 1, 100, device=device)
else:
# Just start and end points
t_span = torch.tensor([0.0, 1.0], device=device)
# Solve ODE
trajectory = odeint(
velocity_fn,
x_0,
t_span,
rtol=rtol,
atol=atol,
method=method
)
# Extract final state
x_final = trajectory[-1]
if return_intermediates:
# Convert trajectory to list of (t, x) tuples
intermediates = [(t.item(), x.cpu()) for t, x in zip(t_span, trajectory)]
return x_final, intermediates
return x_final
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