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afe65cf | 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 | import numpy as np
import abc
import functools
class SDE(abc.ABC):
"""SDE abstract class. Functions are designed for a mini-batch of inputs."""
def __init__(self, N):
"""Construct an SDE.
Args:
N: number of discretization time steps.
"""
super().__init__()
self.N = N
@property
@abc.abstractmethod
def T(self):
"""End time of the SDE."""
pass
@abc.abstractmethod
def sde(self, x, t):
pass
@abc.abstractmethod
def marginal_prob(self, x, t):
"""Parameters to determine the marginal distribution of the SDE, $p_t(x)$."""
pass
@abc.abstractmethod
def prior_sampling(self, rng, shape):
"""Generate one sample from the prior distribution, $p_T(x)$."""
pass
def reverse(self, score_fn, probability_flow=False):
"""Create the reverse-time SDE/ODE.
Args:
score_fn: A time-dependent score-based model that takes x and t and returns the score.
probability_flow: If `True`, create the reverse-time ODE used for probability flow sampling.
"""
N = self.N
T = self.T
sde_fn = self.sde
# Build the class for reverse-time SDE.
class RSDE(self.__class__):
def __init__(self):
self.N = N
self.probability_flow = probability_flow
@property
def T(self):
return T
def sde(self, x, t):
"""Create the drift and diffusion functions for the reverse SDE/ODE."""
drift, diffusion = sde_fn(x, t)
score = score_fn(y=x, t=t)
score = score_fn(y=x, t=t)
drift = drift - (diffusion ** 2)*(score * (0.5 if self.probability_flow else 1.))
# Set the diffusion function to zero for ODEs.
diffusion = np.zeros_like(diffusion) if self.probability_flow else diffusion
return drift, diffusion
return RSDE()
class VPSDE(SDE):
def __init__(self, beta_min=0.1, beta_max=20, N=1000):
"""Construct a Variance Preserving SDE.
Args:
beta_min: value of beta(0)
beta_max: value of beta(1)
N: number of discretization steps
"""
super().__init__(N)
self.beta_0 = beta_min
self.beta_1 = beta_max
self.N = N
self.discrete_betas = np.linspace(beta_min / N, beta_max / N, N)
self.alphas = 1. - self.discrete_betas
self.alphas_cumprod = np.cumprod(self.alphas, axis=0)
self.sqrt_alphas_cumprod = np.sqrt(self.alphas_cumprod)
self.sqrt_1m_alphas_cumprod = np.sqrt(1. - self.alphas_cumprod)
@property
def T(self):
return 1
def sde(self, x, t):
beta_t = self.beta_0 + t * (self.beta_1 - self.beta_0)
drift = -0.5 * beta_t * x
diffusion = np.sqrt(beta_t)
return drift, diffusion
def marginal_prob(self, x, t):
log_mean_coeff = -0.25 * t ** 2 * (self.beta_1 - self.beta_0) - 0.5 * t * self.beta_0
mean = np.exp(log_mean_coeff)*x
std = np.sqrt(1 - np.exp(2. * log_mean_coeff))
return mean, std
def marginal_prob_coef(self, x, t):
log_mean_coeff = -0.25 * t ** 2 * (self.beta_1 - self.beta_0) - 0.5 * t * self.beta_0
mean = np.exp(log_mean_coeff)
std = np.sqrt(1 - np.exp(2. * log_mean_coeff))
return mean, std
def prior_sampling(self, shape):
return np.random.normal(size=shape)
class Predictor(abc.ABC):
"""The abstract class for a predictor algorithm."""
def __init__(self, sde, score_fn):
super().__init__()
self.sde = sde
# Compute the reverse SDE/ODE
self.rsde = sde.reverse(score_fn)
self.score_fn = score_fn
@abc.abstractmethod
def update_fn(self, x, t):
pass
class EulerMaruyamaPredictor(Predictor):
def __init__(self, sde, score_fn):
super().__init__(sde, score_fn)
def update_fn(self, x, t, h):
my_sde = self.rsde.sde
z = self.sde.prior_sampling(x.shape)
drift, diffusion = my_sde(x, t)
x_mean = x - drift * h
x = x_mean + diffusion*np.sqrt(h)*z
return x, x_mean
def shared_predictor_update_fn(x, t, h=None, sde=None, score_fn=None,):
"""A wrapper that configures and returns the update function of predictors."""
predictor_obj = EulerMaruyamaPredictor(sde, score_fn)
return predictor_obj.update_fn(x, t, h)
# VP sampler
def get_pc_sampler(score_fn, sde, denoise=True, eps=1e-3, repaint=False):
predictor_update_fn = functools.partial(shared_predictor_update_fn,
sde=sde,
score_fn=score_fn)
def pc_sampler(prior, r=5, j=5):
# Initial sample
x = prior
timesteps = np.linspace(sde.T, eps, sde.N)
h = timesteps - np.append(timesteps, 0)[1:] # true step-size: difference between current time and next time (only the new predictor classes will use h, others will ignore)
N = sde.N - 1
for i in range(N):
x, x_mean = predictor_update_fn(x, timesteps[i], h[i])
if denoise: # Tweedie formula
u, std = sde.marginal_prob(x, eps)
x = x + (std ** 2)*score_fn(y=x, t=eps)
return x
def pc_sampler_repaint(prior, r=5, j=5):
# Initial sample
x = prior
timesteps = np.linspace(sde.T, eps, sde.N)
h = timesteps - np.append(timesteps, 0)[1:] # true step-size: difference between current time and next time (only the new predictor classes will use h, others will ignore)
N = sde.N - 1
i_repaint = 0
i = 0
while i < N:
x, x_mean = predictor_update_fn(x, timesteps[i], h[i])
if i_repaint < r-1 and (i+1) % j == 0: # we did j iterations, but not enough repaint, we must repaint again
# Going backward in time; using Euler-Maruyama
z = sde.prior_sampling(x.shape)
drift, diffusion = sde.sde(x, timesteps[i])
h_ = sum(h[(i-j+1):(i+1)])
x_mean = x + drift * h_
x = x_mean + diffusion*np.sqrt(h_)*z
# iterate back
i_repaint = i_repaint + 1
i = i - j
elif i_repaint == r-1 and (i+1) % j == 0: # we did j iterations and enough repaint, we continue and reset the repaint counter
i_repaint = 0
i = i + 1
if denoise: # Tweedie formula
u, std = sde.marginal_prob(x, eps)
x = x + (std ** 2)*score_fn(y=x, t=eps)
return x
if repaint:
return pc_sampler_repaint
else:
return pc_sampler
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