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September 9, 2024 17:40
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flow matching in 60 line of code
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| import torch | |
| import torch.nn as nn | |
| from sklearn.datasets import make_moons | |
| from tqdm import tqdm | |
| import matplotlib.pyplot as plt | |
| class Flow(nn.Module): | |
| def __init__(self, n_dim=2, n_pos_dim=2, n_hidden=64): | |
| super().__init__() | |
| self.n_dim = n_dim | |
| self.n_pos_dim = n_pos_dim | |
| self.net = nn.Sequential( | |
| nn.Linear(n_dim + n_pos_dim, n_hidden), nn.ELU(), | |
| nn.Linear(n_hidden, n_hidden), nn.ELU(), | |
| nn.Linear(n_hidden, n_hidden), nn.ELU(), | |
| nn.Linear(n_hidden, n_dim)) | |
| self.temb = nn.Linear(1, n_pos_dim//2) | |
| def forward(self, t, x): | |
| t = self.temb(t).mul(torch.pi) | |
| t = torch.cat((t.cos(), t.sin()), dim=-1) | |
| return self.net(torch.cat((t, x), dim=-1)) | |
| def loss(self, x): | |
| time = torch.rand(len(x), 1) | |
| noise = torch.randn_like(x) | |
| noisedx = (1 - time) * x + (0.001 + 0.999 * time) * noise | |
| target = noise.mul(0.999).sub(x) | |
| prediction = self.forward(time, noisedx) | |
| return (prediction - target).square().mean() | |
| def sample(self, n_samples, n_steps=100): | |
| x = torch.randn((n_samples, self.n_dim)) | |
| dt = 1.0 / n_steps | |
| with torch.no_grad(): # runge-kutta-4 diffeq solver | |
| for t in tqdm(torch.linspace(1, 0, n_steps)): | |
| t = t.expand(len(x), 1) | |
| k1 = self.forward(t, x) | |
| k2 = self.forward(t - dt/2, x - (dt*k1)/2) | |
| k3 = self.forward(t - dt/2, x - (dt*k2)/2) | |
| k4 = self.forward(t - dt, x - dt*k3) | |
| x = x - (dt / 6) * (k1 + 2*k2 + 2*k3 + k4) | |
| return x | |
| data, _ = make_moons(16384, noise=0.05) | |
| data = torch.from_numpy(data).float() | |
| flow = Flow() | |
| optimizer = torch.optim.Adam(flow.parameters(), lr=1e-3) | |
| for epoch in tqdm(range(16384)): | |
| subset = torch.randint(0, len(data), (256,)) | |
| x = data[subset] | |
| flow.loss(x).backward() | |
| optimizer.step() | |
| optimizer.zero_grad() | |
| xhat = flow.sample(16384) | |
| plt.figure(figsize=(4.8, 4.8), dpi=150) | |
| plt.hist2d(*xhat.T, bins=128) |
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