File size: 14,562 Bytes
5085882 |
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 |
import torch as th
import numpy as np
import logging
import enum
from . import path
from .utils import EasyDict, log_state, mean_flat
from .integrators import ode, sde
class ModelType(enum.Enum):
"""
Which type of output the model predicts.
"""
NOISE = enum.auto() # the model predicts epsilon
SCORE = enum.auto() # the model predicts \nabla \log p(x)
VELOCITY = enum.auto() # the model predicts v(x)
class PathType(enum.Enum):
"""
Which type of path to use.
"""
LINEAR = enum.auto()
GVP = enum.auto()
VP = enum.auto()
class WeightType(enum.Enum):
"""
Which type of weighting to use.
"""
NONE = enum.auto()
VELOCITY = enum.auto()
LIKELIHOOD = enum.auto()
class Transport:
def __init__(
self,
*,
model_type,
path_type,
loss_type,
train_eps,
sample_eps,
):
path_options = {
PathType.LINEAR: path.ICPlan,
PathType.GVP: path.GVPCPlan,
PathType.VP: path.VPCPlan,
}
self.loss_type = loss_type
self.model_type = model_type
self.path_sampler = path_options[path_type]()
self.train_eps = train_eps
self.sample_eps = sample_eps
def prior_logp(self, z):
'''
Standard multivariate normal prior
Assume z is batched
'''
shape = th.tensor(z.size())
N = th.prod(shape[1:])
_fn = lambda x: -N / 2. * np.log(2 * np.pi) - th.sum(x ** 2) / 2.
return th.vmap(_fn)(z)
def check_interval(
self,
train_eps,
sample_eps,
*,
diffusion_form="SBDM",
sde=False,
reverse=False,
eval=False,
last_step_size=0.0,
):
t0 = 0
t1 = 1
eps = train_eps if not eval else sample_eps
if (type(self.path_sampler) in [path.VPCPlan]):
t1 = 1 - eps if (not sde or last_step_size == 0) else 1 - last_step_size
elif (type(self.path_sampler) in [path.ICPlan, path.GVPCPlan]) \
and (self.model_type != ModelType.VELOCITY or sde): # avoid numerical issue by taking a first semi-implicit step
t0 = eps if (diffusion_form == "SBDM" and sde) or self.model_type != ModelType.VELOCITY else 0
t1 = 1 - eps if (not sde or last_step_size == 0) else 1 - last_step_size
if reverse:
t0, t1 = 1 - t0, 1 - t1
return t0, t1
def sample(self, x1):
"""Sampling x0 & t based on shape of x1 (if needed)
Args:
x1 - data point; [batch, *dim]
"""
x0 = th.randn_like(x1)
t0, t1 = self.check_interval(self.train_eps, self.sample_eps)
t = th.rand((x1.shape[0],)) * (t1 - t0) + t0
t = t.to(x1)
return t, x0, x1
def training_losses(
self,
model,
x1,
model_kwargs=None
):
"""Loss for training the score model
Args:
- model: backbone model; could be score, noise, or velocity
- x1: datapoint
- model_kwargs: additional arguments for the model
"""
if model_kwargs == None:
model_kwargs = {}
t, x0, x1 = self.sample(x1)
t, xt, ut = self.path_sampler.plan(t, x0, x1)
model_output = model(xt, t, **model_kwargs)
B, *_, C = xt.shape
assert model_output.size() == (B, *xt.size()[1:-1], C)
terms = {}
terms['pred'] = model_output
if self.model_type == ModelType.VELOCITY:
terms['loss'] = mean_flat(((model_output - ut) ** 2))
else:
_, drift_var = self.path_sampler.compute_drift(xt, t)
sigma_t, _ = self.path_sampler.compute_sigma_t(path.expand_t_like_x(t, xt))
if self.loss_type in [WeightType.VELOCITY]:
weight = (drift_var / sigma_t) ** 2
elif self.loss_type in [WeightType.LIKELIHOOD]:
weight = drift_var / (sigma_t ** 2)
elif self.loss_type in [WeightType.NONE]:
weight = 1
else:
raise NotImplementedError()
if self.model_type == ModelType.NOISE:
terms['loss'] = mean_flat(weight * ((model_output - x0) ** 2))
else:
terms['loss'] = mean_flat(weight * ((model_output * sigma_t + x0) ** 2))
return terms
def get_drift(
self
):
"""member function for obtaining the drift of the probability flow ODE"""
def score_ode(x, t, model, **model_kwargs):
drift_mean, drift_var = self.path_sampler.compute_drift(x, t)
model_output = model(x, t, **model_kwargs)
return (-drift_mean + drift_var * model_output) # by change of variable
def noise_ode(x, t, model, **model_kwargs):
drift_mean, drift_var = self.path_sampler.compute_drift(x, t)
sigma_t, _ = self.path_sampler.compute_sigma_t(path.expand_t_like_x(t, x))
model_output = model(x, t, **model_kwargs)
score = model_output / -sigma_t
return (-drift_mean + drift_var * score)
def velocity_ode(x, t, model, **model_kwargs):
model_output = model(x, t, **model_kwargs)
return model_output
if self.model_type == ModelType.NOISE:
drift_fn = noise_ode
elif self.model_type == ModelType.SCORE:
drift_fn = score_ode
else:
drift_fn = velocity_ode
def body_fn(x, t, model, **model_kwargs):
model_output = drift_fn(x, t, model, **model_kwargs)
assert model_output.shape == x.shape, "Output shape from ODE solver must match input shape"
return model_output
return body_fn
def get_score(
self,
):
"""member function for obtaining score of
x_t = alpha_t * x + sigma_t * eps"""
if self.model_type == ModelType.NOISE:
score_fn = lambda x, t, model, **kwargs: model(x, t, **kwargs) / -self.path_sampler.compute_sigma_t(path.expand_t_like_x(t, x))[0]
elif self.model_type == ModelType.SCORE:
score_fn = lambda x, t, model, **kwagrs: model(x, t, **kwagrs)
elif self.model_type == ModelType.VELOCITY:
score_fn = lambda x, t, model, **kwargs: self.path_sampler.get_score_from_velocity(model(x, t, **kwargs), x, t)
else:
raise NotImplementedError()
return score_fn
class Sampler:
"""Sampler class for the transport model"""
def __init__(
self,
transport,
):
"""Constructor for a general sampler; supporting different sampling methods
Args:
- transport: an tranport object specify model prediction & interpolant type
"""
self.transport = transport
self.drift = self.transport.get_drift()
self.score = self.transport.get_score()
def __get_sde_diffusion_and_drift(
self,
*,
diffusion_form="SBDM",
diffusion_norm=1.0,
):
def diffusion_fn(x, t):
diffusion = self.transport.path_sampler.compute_diffusion(x, t, form=diffusion_form, norm=diffusion_norm)
return diffusion
sde_drift = \
lambda x, t, model, **kwargs: \
self.drift(x, t, model, **kwargs) + diffusion_fn(x, t) * self.score(x, t, model, **kwargs)
sde_diffusion = diffusion_fn
return sde_drift, sde_diffusion
def __get_last_step(
self,
sde_drift,
*,
last_step,
last_step_size,
):
"""Get the last step function of the SDE solver"""
if last_step is None:
last_step_fn = \
lambda x, t, model, **model_kwargs: \
x
elif last_step == "Mean":
last_step_fn = \
lambda x, t, model, **model_kwargs: \
x + sde_drift(x, t, model, **model_kwargs) * last_step_size
elif last_step == "Tweedie":
alpha = self.transport.path_sampler.compute_alpha_t # simple aliasing; the original name was too long
sigma = self.transport.path_sampler.compute_sigma_t
last_step_fn = \
lambda x, t, model, **model_kwargs: \
x / alpha(t)[0][0] + (sigma(t)[0][0] ** 2) / alpha(t)[0][0] * self.score(x, t, model, **model_kwargs)
elif last_step == "Euler":
last_step_fn = \
lambda x, t, model, **model_kwargs: \
x + self.drift(x, t, model, **model_kwargs) * last_step_size
else:
raise NotImplementedError()
return last_step_fn
def sample_sde(
self,
*,
sampling_method="Euler",
diffusion_form="SBDM",
diffusion_norm=1.0,
last_step="Mean",
last_step_size=0.04,
num_steps=250,
):
"""returns a sampling function with given SDE settings
Args:
- sampling_method: type of sampler used in solving the SDE; default to be Euler-Maruyama
- diffusion_form: function form of diffusion coefficient; default to be matching SBDM
- diffusion_norm: function magnitude of diffusion coefficient; default to 1
- last_step: type of the last step; default to identity
- last_step_size: size of the last step; default to match the stride of 250 steps over [0,1]
- num_steps: total integration step of SDE
"""
if last_step is None:
last_step_size = 0.0
sde_drift, sde_diffusion = self.__get_sde_diffusion_and_drift(
diffusion_form=diffusion_form,
diffusion_norm=diffusion_norm,
)
t0, t1 = self.transport.check_interval(
self.transport.train_eps,
self.transport.sample_eps,
diffusion_form=diffusion_form,
sde=True,
eval=True,
reverse=False,
last_step_size=last_step_size,
)
_sde = sde(
sde_drift,
sde_diffusion,
t0=t0,
t1=t1,
num_steps=num_steps,
sampler_type=sampling_method
)
last_step_fn = self.__get_last_step(sde_drift, last_step=last_step, last_step_size=last_step_size)
def _sample(init, model, **model_kwargs):
xs = _sde.sample(init, model, **model_kwargs)
ts = th.ones(init.size(0), device=init.device) * t1
x = last_step_fn(xs[-1], ts, model, **model_kwargs)
xs.append(x)
assert len(xs) == num_steps, "Samples does not match the number of steps"
return xs
return _sample
def sample_ode(
self,
*,
sampling_method="dopri5",
num_steps=50,
atol=1e-6,
rtol=1e-3,
reverse=False,
):
"""returns a sampling function with given ODE settings
Args:
- sampling_method: type of sampler used in solving the ODE; default to be Dopri5
- num_steps:
- fixed solver (Euler, Heun): the actual number of integration steps performed
- adaptive solver (Dopri5): the number of datapoints saved during integration; produced by interpolation
- atol: absolute error tolerance for the solver
- rtol: relative error tolerance for the solver
- reverse: whether solving the ODE in reverse (data to noise); default to False
"""
if reverse:
drift = lambda x, t, model, **kwargs: self.drift(x, th.ones_like(t) * (1 - t), model, **kwargs)
else:
drift = self.drift
t0, t1 = self.transport.check_interval(
self.transport.train_eps,
self.transport.sample_eps,
sde=False,
eval=True,
reverse=reverse,
last_step_size=0.0,
)
_ode = ode(
drift=drift,
t0=t0,
t1=t1,
sampler_type=sampling_method,
num_steps=num_steps,
atol=atol,
rtol=rtol,
)
return _ode.sample
def sample_ode_likelihood(
self,
*,
sampling_method="dopri5",
num_steps=50,
atol=1e-6,
rtol=1e-3,
):
"""returns a sampling function for calculating likelihood with given ODE settings
Args:
- sampling_method: type of sampler used in solving the ODE; default to be Dopri5
- num_steps:
- fixed solver (Euler, Heun): the actual number of integration steps performed
- adaptive solver (Dopri5): the number of datapoints saved during integration; produced by interpolation
- atol: absolute error tolerance for the solver
- rtol: relative error tolerance for the solver
"""
def _likelihood_drift(x, t, model, **model_kwargs):
x, _ = x
eps = th.randint(2, x.size(), dtype=th.float, device=x.device) * 2 - 1
t = th.ones_like(t) * (1 - t)
with th.enable_grad():
x.requires_grad = True
grad = th.autograd.grad(th.sum(self.drift(x, t, model, **model_kwargs) * eps), x)[0]
logp_grad = th.sum(grad * eps, dim=tuple(range(1, len(x.size()))))
drift = self.drift(x, t, model, **model_kwargs)
return (-drift, logp_grad)
t0, t1 = self.transport.check_interval(
self.transport.train_eps,
self.transport.sample_eps,
sde=False,
eval=True,
reverse=False,
last_step_size=0.0,
)
_ode = ode(
drift=_likelihood_drift,
t0=t0,
t1=t1,
sampler_type=sampling_method,
num_steps=num_steps,
atol=atol,
rtol=rtol,
)
def _sample_fn(x, model, **model_kwargs):
init_logp = th.zeros(x.size(0)).to(x)
input = (x, init_logp)
drift, delta_logp = _ode.sample(input, model, **model_kwargs)
drift, delta_logp = drift[-1], delta_logp[-1]
prior_logp = self.transport.prior_logp(drift)
logp = prior_logp - delta_logp
return logp, drift
return _sample_fn |