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# Better Flow Matching UniPC by Lvmin Zhang
# (c) 2025
# CC BY-SA 4.0
# Attribution-ShareAlike 4.0 International Licence
import torch
from tqdm.auto import trange
def expand_dims(v, dims):
return v[(...,) + (None,) * (dims - 1)]
class FlowMatchUniPC:
def __init__(self, model, extra_args, variant='bh1'):
self.model = model
self.variant = variant
self.extra_args = extra_args
def model_fn(self, x, t):
return self.model(x, t, **self.extra_args)
def update_fn(self, x, model_prev_list, t_prev_list, t, order):
assert order <= len(model_prev_list)
dims = x.dim()
t_prev_0 = t_prev_list[-1]
lambda_prev_0 = - torch.log(t_prev_0)
lambda_t = - torch.log(t)
model_prev_0 = model_prev_list[-1]
h = lambda_t - lambda_prev_0
rks = []
D1s = []
for i in range(1, order):
t_prev_i = t_prev_list[-(i + 1)]
model_prev_i = model_prev_list[-(i + 1)]
lambda_prev_i = - torch.log(t_prev_i)
rk = ((lambda_prev_i - lambda_prev_0) / h)[0]
rks.append(rk)
D1s.append((model_prev_i - model_prev_0) / rk)
rks.append(1.)
rks = torch.tensor(rks, device=x.device)
R = []
b = []
hh = -h[0]
h_phi_1 = torch.expm1(hh)
h_phi_k = h_phi_1 / hh - 1
factorial_i = 1
if self.variant == 'bh1':
B_h = hh
elif self.variant == 'bh2':
B_h = torch.expm1(hh)
else:
raise NotImplementedError('Bad variant!')
for i in range(1, order + 1):
R.append(torch.pow(rks, i - 1))
b.append(h_phi_k * factorial_i / B_h)
factorial_i *= (i + 1)
h_phi_k = h_phi_k / hh - 1 / factorial_i
R = torch.stack(R)
b = torch.tensor(b, device=x.device)
use_predictor = len(D1s) > 0
if use_predictor:
D1s = torch.stack(D1s, dim=1)
if order == 2:
rhos_p = torch.tensor([0.5], device=b.device)
else:
rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1])
else:
D1s = None
rhos_p = None
if order == 1:
rhos_c = torch.tensor([0.5], device=b.device)
else:
rhos_c = torch.linalg.solve(R, b)
x_t_ = expand_dims(t / t_prev_0, dims) * x - expand_dims(h_phi_1, dims) * model_prev_0
if use_predictor:
pred_res = torch.tensordot(D1s, rhos_p, dims=([1], [0]))
else:
pred_res = 0
x_t = x_t_ - expand_dims(B_h, dims) * pred_res
model_t = self.model_fn(x_t, t)
if D1s is not None:
corr_res = torch.tensordot(D1s, rhos_c[:-1], dims=([1], [0]))
else:
corr_res = 0
D1_t = (model_t - model_prev_0)
x_t = x_t_ - expand_dims(B_h, dims) * (corr_res + rhos_c[-1] * D1_t)
return x_t, model_t
def sample(self, x, sigmas, callback=None, disable_pbar=False):
order = min(3, len(sigmas) - 2)
model_prev_list, t_prev_list = [], []
for i in trange(len(sigmas) - 1, disable=disable_pbar):
vec_t = sigmas[i].expand(x.shape[0])
if i == 0:
model_prev_list = [self.model_fn(x, vec_t)]
t_prev_list = [vec_t]
elif i < order:
init_order = i
x, model_x = self.update_fn(x, model_prev_list, t_prev_list, vec_t, init_order)
model_prev_list.append(model_x)
t_prev_list.append(vec_t)
else:
x, model_x = self.update_fn(x, model_prev_list, t_prev_list, vec_t, order)
model_prev_list.append(model_x)
t_prev_list.append(vec_t)
model_prev_list = model_prev_list[-order:]
t_prev_list = t_prev_list[-order:]
if callback is not None:
callback({'x': x, 'i': i, 'denoised': model_prev_list[-1]})
return model_prev_list[-1]
def sample_unipc(model, noise, sigmas, extra_args=None, callback=None, disable=False, variant='bh1'):
assert variant in ['bh1', 'bh2']
return FlowMatchUniPC(model, extra_args=extra_args, variant=variant).sample(noise, sigmas=sigmas, callback=callback, disable_pbar=disable)
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