Delete modules/uni_pc/uni_pc.py
Browse files- modules/uni_pc/uni_pc.py +0 -863
modules/uni_pc/uni_pc.py
DELETED
@@ -1,863 +0,0 @@
|
|
1 |
-
import torch
|
2 |
-
import math
|
3 |
-
import tqdm
|
4 |
-
|
5 |
-
|
6 |
-
class NoiseScheduleVP:
|
7 |
-
def __init__(
|
8 |
-
self,
|
9 |
-
schedule='discrete',
|
10 |
-
betas=None,
|
11 |
-
alphas_cumprod=None,
|
12 |
-
continuous_beta_0=0.1,
|
13 |
-
continuous_beta_1=20.,
|
14 |
-
):
|
15 |
-
"""Create a wrapper class for the forward SDE (VP type).
|
16 |
-
|
17 |
-
***
|
18 |
-
Update: We support discrete-time diffusion models by implementing a picewise linear interpolation for log_alpha_t.
|
19 |
-
We recommend to use schedule='discrete' for the discrete-time diffusion models, especially for high-resolution images.
|
20 |
-
***
|
21 |
-
|
22 |
-
The forward SDE ensures that the condition distribution q_{t|0}(x_t | x_0) = N ( alpha_t * x_0, sigma_t^2 * I ).
|
23 |
-
We further define lambda_t = log(alpha_t) - log(sigma_t), which is the half-logSNR (described in the DPM-Solver paper).
|
24 |
-
Therefore, we implement the functions for computing alpha_t, sigma_t and lambda_t. For t in [0, T], we have:
|
25 |
-
|
26 |
-
log_alpha_t = self.marginal_log_mean_coeff(t)
|
27 |
-
sigma_t = self.marginal_std(t)
|
28 |
-
lambda_t = self.marginal_lambda(t)
|
29 |
-
|
30 |
-
Moreover, as lambda(t) is an invertible function, we also support its inverse function:
|
31 |
-
|
32 |
-
t = self.inverse_lambda(lambda_t)
|
33 |
-
|
34 |
-
===============================================================
|
35 |
-
|
36 |
-
We support both discrete-time DPMs (trained on n = 0, 1, ..., N-1) and continuous-time DPMs (trained on t in [t_0, T]).
|
37 |
-
|
38 |
-
1. For discrete-time DPMs:
|
39 |
-
|
40 |
-
For discrete-time DPMs trained on n = 0, 1, ..., N-1, we convert the discrete steps to continuous time steps by:
|
41 |
-
t_i = (i + 1) / N
|
42 |
-
e.g. for N = 1000, we have t_0 = 1e-3 and T = t_{N-1} = 1.
|
43 |
-
We solve the corresponding diffusion ODE from time T = 1 to time t_0 = 1e-3.
|
44 |
-
|
45 |
-
Args:
|
46 |
-
betas: A `torch.Tensor`. The beta array for the discrete-time DPM. (See the original DDPM paper for details)
|
47 |
-
alphas_cumprod: A `torch.Tensor`. The cumprod alphas for the discrete-time DPM. (See the original DDPM paper for details)
|
48 |
-
|
49 |
-
Note that we always have alphas_cumprod = cumprod(betas). Therefore, we only need to set one of `betas` and `alphas_cumprod`.
|
50 |
-
|
51 |
-
**Important**: Please pay special attention for the args for `alphas_cumprod`:
|
52 |
-
The `alphas_cumprod` is the \hat{alpha_n} arrays in the notations of DDPM. Specifically, DDPMs assume that
|
53 |
-
q_{t_n | 0}(x_{t_n} | x_0) = N ( \sqrt{\hat{alpha_n}} * x_0, (1 - \hat{alpha_n}) * I ).
|
54 |
-
Therefore, the notation \hat{alpha_n} is different from the notation alpha_t in DPM-Solver. In fact, we have
|
55 |
-
alpha_{t_n} = \sqrt{\hat{alpha_n}},
|
56 |
-
and
|
57 |
-
log(alpha_{t_n}) = 0.5 * log(\hat{alpha_n}).
|
58 |
-
|
59 |
-
|
60 |
-
2. For continuous-time DPMs:
|
61 |
-
|
62 |
-
We support two types of VPSDEs: linear (DDPM) and cosine (improved-DDPM). The hyperparameters for the noise
|
63 |
-
schedule are the default settings in DDPM and improved-DDPM:
|
64 |
-
|
65 |
-
Args:
|
66 |
-
beta_min: A `float` number. The smallest beta for the linear schedule.
|
67 |
-
beta_max: A `float` number. The largest beta for the linear schedule.
|
68 |
-
cosine_s: A `float` number. The hyperparameter in the cosine schedule.
|
69 |
-
cosine_beta_max: A `float` number. The hyperparameter in the cosine schedule.
|
70 |
-
T: A `float` number. The ending time of the forward process.
|
71 |
-
|
72 |
-
===============================================================
|
73 |
-
|
74 |
-
Args:
|
75 |
-
schedule: A `str`. The noise schedule of the forward SDE. 'discrete' for discrete-time DPMs,
|
76 |
-
'linear' or 'cosine' for continuous-time DPMs.
|
77 |
-
Returns:
|
78 |
-
A wrapper object of the forward SDE (VP type).
|
79 |
-
|
80 |
-
===============================================================
|
81 |
-
|
82 |
-
Example:
|
83 |
-
|
84 |
-
# For discrete-time DPMs, given betas (the beta array for n = 0, 1, ..., N - 1):
|
85 |
-
>>> ns = NoiseScheduleVP('discrete', betas=betas)
|
86 |
-
|
87 |
-
# For discrete-time DPMs, given alphas_cumprod (the \hat{alpha_n} array for n = 0, 1, ..., N - 1):
|
88 |
-
>>> ns = NoiseScheduleVP('discrete', alphas_cumprod=alphas_cumprod)
|
89 |
-
|
90 |
-
# For continuous-time DPMs (VPSDE), linear schedule:
|
91 |
-
>>> ns = NoiseScheduleVP('linear', continuous_beta_0=0.1, continuous_beta_1=20.)
|
92 |
-
|
93 |
-
"""
|
94 |
-
|
95 |
-
if schedule not in ['discrete', 'linear', 'cosine']:
|
96 |
-
raise ValueError(f"Unsupported noise schedule {schedule}. The schedule needs to be 'discrete' or 'linear' or 'cosine'")
|
97 |
-
|
98 |
-
self.schedule = schedule
|
99 |
-
if schedule == 'discrete':
|
100 |
-
if betas is not None:
|
101 |
-
log_alphas = 0.5 * torch.log(1 - betas).cumsum(dim=0)
|
102 |
-
else:
|
103 |
-
assert alphas_cumprod is not None
|
104 |
-
log_alphas = 0.5 * torch.log(alphas_cumprod)
|
105 |
-
self.total_N = len(log_alphas)
|
106 |
-
self.T = 1.
|
107 |
-
self.t_array = torch.linspace(0., 1., self.total_N + 1)[1:].reshape((1, -1))
|
108 |
-
self.log_alpha_array = log_alphas.reshape((1, -1,))
|
109 |
-
else:
|
110 |
-
self.total_N = 1000
|
111 |
-
self.beta_0 = continuous_beta_0
|
112 |
-
self.beta_1 = continuous_beta_1
|
113 |
-
self.cosine_s = 0.008
|
114 |
-
self.cosine_beta_max = 999.
|
115 |
-
self.cosine_t_max = math.atan(self.cosine_beta_max * (1. + self.cosine_s) / math.pi) * 2. * (1. + self.cosine_s) / math.pi - self.cosine_s
|
116 |
-
self.cosine_log_alpha_0 = math.log(math.cos(self.cosine_s / (1. + self.cosine_s) * math.pi / 2.))
|
117 |
-
self.schedule = schedule
|
118 |
-
if schedule == 'cosine':
|
119 |
-
# For the cosine schedule, T = 1 will have numerical issues. So we manually set the ending time T.
|
120 |
-
# Note that T = 0.9946 may be not the optimal setting. However, we find it works well.
|
121 |
-
self.T = 0.9946
|
122 |
-
else:
|
123 |
-
self.T = 1.
|
124 |
-
|
125 |
-
def marginal_log_mean_coeff(self, t):
|
126 |
-
"""
|
127 |
-
Compute log(alpha_t) of a given continuous-time label t in [0, T].
|
128 |
-
"""
|
129 |
-
if self.schedule == 'discrete':
|
130 |
-
return interpolate_fn(t.reshape((-1, 1)), self.t_array.to(t.device), self.log_alpha_array.to(t.device)).reshape((-1))
|
131 |
-
elif self.schedule == 'linear':
|
132 |
-
return -0.25 * t ** 2 * (self.beta_1 - self.beta_0) - 0.5 * t * self.beta_0
|
133 |
-
elif self.schedule == 'cosine':
|
134 |
-
log_alpha_fn = lambda s: torch.log(torch.cos((s + self.cosine_s) / (1. + self.cosine_s) * math.pi / 2.))
|
135 |
-
log_alpha_t = log_alpha_fn(t) - self.cosine_log_alpha_0
|
136 |
-
return log_alpha_t
|
137 |
-
|
138 |
-
def marginal_alpha(self, t):
|
139 |
-
"""
|
140 |
-
Compute alpha_t of a given continuous-time label t in [0, T].
|
141 |
-
"""
|
142 |
-
return torch.exp(self.marginal_log_mean_coeff(t))
|
143 |
-
|
144 |
-
def marginal_std(self, t):
|
145 |
-
"""
|
146 |
-
Compute sigma_t of a given continuous-time label t in [0, T].
|
147 |
-
"""
|
148 |
-
return torch.sqrt(1. - torch.exp(2. * self.marginal_log_mean_coeff(t)))
|
149 |
-
|
150 |
-
def marginal_lambda(self, t):
|
151 |
-
"""
|
152 |
-
Compute lambda_t = log(alpha_t) - log(sigma_t) of a given continuous-time label t in [0, T].
|
153 |
-
"""
|
154 |
-
log_mean_coeff = self.marginal_log_mean_coeff(t)
|
155 |
-
log_std = 0.5 * torch.log(1. - torch.exp(2. * log_mean_coeff))
|
156 |
-
return log_mean_coeff - log_std
|
157 |
-
|
158 |
-
def inverse_lambda(self, lamb):
|
159 |
-
"""
|
160 |
-
Compute the continuous-time label t in [0, T] of a given half-logSNR lambda_t.
|
161 |
-
"""
|
162 |
-
if self.schedule == 'linear':
|
163 |
-
tmp = 2. * (self.beta_1 - self.beta_0) * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb))
|
164 |
-
Delta = self.beta_0**2 + tmp
|
165 |
-
return tmp / (torch.sqrt(Delta) + self.beta_0) / (self.beta_1 - self.beta_0)
|
166 |
-
elif self.schedule == 'discrete':
|
167 |
-
log_alpha = -0.5 * torch.logaddexp(torch.zeros((1,)).to(lamb.device), -2. * lamb)
|
168 |
-
t = interpolate_fn(log_alpha.reshape((-1, 1)), torch.flip(self.log_alpha_array.to(lamb.device), [1]), torch.flip(self.t_array.to(lamb.device), [1]))
|
169 |
-
return t.reshape((-1,))
|
170 |
-
else:
|
171 |
-
log_alpha = -0.5 * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb))
|
172 |
-
t_fn = lambda log_alpha_t: torch.arccos(torch.exp(log_alpha_t + self.cosine_log_alpha_0)) * 2. * (1. + self.cosine_s) / math.pi - self.cosine_s
|
173 |
-
t = t_fn(log_alpha)
|
174 |
-
return t
|
175 |
-
|
176 |
-
|
177 |
-
def model_wrapper(
|
178 |
-
model,
|
179 |
-
noise_schedule,
|
180 |
-
model_type="noise",
|
181 |
-
model_kwargs=None,
|
182 |
-
guidance_type="uncond",
|
183 |
-
#condition=None,
|
184 |
-
#unconditional_condition=None,
|
185 |
-
guidance_scale=1.,
|
186 |
-
classifier_fn=None,
|
187 |
-
classifier_kwargs=None,
|
188 |
-
):
|
189 |
-
"""Create a wrapper function for the noise prediction model.
|
190 |
-
|
191 |
-
DPM-Solver needs to solve the continuous-time diffusion ODEs. For DPMs trained on discrete-time labels, we need to
|
192 |
-
firstly wrap the model function to a noise prediction model that accepts the continuous time as the input.
|
193 |
-
|
194 |
-
We support four types of the diffusion model by setting `model_type`:
|
195 |
-
|
196 |
-
1. "noise": noise prediction model. (Trained by predicting noise).
|
197 |
-
|
198 |
-
2. "x_start": data prediction model. (Trained by predicting the data x_0 at time 0).
|
199 |
-
|
200 |
-
3. "v": velocity prediction model. (Trained by predicting the velocity).
|
201 |
-
The "v" prediction is derivation detailed in Appendix D of [1], and is used in Imagen-Video [2].
|
202 |
-
|
203 |
-
[1] Salimans, Tim, and Jonathan Ho. "Progressive distillation for fast sampling of diffusion models."
|
204 |
-
arXiv preprint arXiv:2202.00512 (2022).
|
205 |
-
[2] Ho, Jonathan, et al. "Imagen Video: High Definition Video Generation with Diffusion Models."
|
206 |
-
arXiv preprint arXiv:2210.02303 (2022).
|
207 |
-
|
208 |
-
4. "score": marginal score function. (Trained by denoising score matching).
|
209 |
-
Note that the score function and the noise prediction model follows a simple relationship:
|
210 |
-
```
|
211 |
-
noise(x_t, t) = -sigma_t * score(x_t, t)
|
212 |
-
```
|
213 |
-
|
214 |
-
We support three types of guided sampling by DPMs by setting `guidance_type`:
|
215 |
-
1. "uncond": unconditional sampling by DPMs.
|
216 |
-
The input `model` has the following format:
|
217 |
-
``
|
218 |
-
model(x, t_input, **model_kwargs) -> noise | x_start | v | score
|
219 |
-
``
|
220 |
-
|
221 |
-
2. "classifier": classifier guidance sampling [3] by DPMs and another classifier.
|
222 |
-
The input `model` has the following format:
|
223 |
-
``
|
224 |
-
model(x, t_input, **model_kwargs) -> noise | x_start | v | score
|
225 |
-
``
|
226 |
-
|
227 |
-
The input `classifier_fn` has the following format:
|
228 |
-
``
|
229 |
-
classifier_fn(x, t_input, cond, **classifier_kwargs) -> logits(x, t_input, cond)
|
230 |
-
``
|
231 |
-
|
232 |
-
[3] P. Dhariwal and A. Q. Nichol, "Diffusion models beat GANs on image synthesis,"
|
233 |
-
in Advances in Neural Information Processing Systems, vol. 34, 2021, pp. 8780-8794.
|
234 |
-
|
235 |
-
3. "classifier-free": classifier-free guidance sampling by conditional DPMs.
|
236 |
-
The input `model` has the following format:
|
237 |
-
``
|
238 |
-
model(x, t_input, cond, **model_kwargs) -> noise | x_start | v | score
|
239 |
-
``
|
240 |
-
And if cond == `unconditional_condition`, the model output is the unconditional DPM output.
|
241 |
-
|
242 |
-
[4] Ho, Jonathan, and Tim Salimans. "Classifier-free diffusion guidance."
|
243 |
-
arXiv preprint arXiv:2207.12598 (2022).
|
244 |
-
|
245 |
-
|
246 |
-
The `t_input` is the time label of the model, which may be discrete-time labels (i.e. 0 to 999)
|
247 |
-
or continuous-time labels (i.e. epsilon to T).
|
248 |
-
|
249 |
-
We wrap the model function to accept only `x` and `t_continuous` as inputs, and outputs the predicted noise:
|
250 |
-
``
|
251 |
-
def model_fn(x, t_continuous) -> noise:
|
252 |
-
t_input = get_model_input_time(t_continuous)
|
253 |
-
return noise_pred(model, x, t_input, **model_kwargs)
|
254 |
-
``
|
255 |
-
where `t_continuous` is the continuous time labels (i.e. epsilon to T). And we use `model_fn` for DPM-Solver.
|
256 |
-
|
257 |
-
===============================================================
|
258 |
-
|
259 |
-
Args:
|
260 |
-
model: A diffusion model with the corresponding format described above.
|
261 |
-
noise_schedule: A noise schedule object, such as NoiseScheduleVP.
|
262 |
-
model_type: A `str`. The parameterization type of the diffusion model.
|
263 |
-
"noise" or "x_start" or "v" or "score".
|
264 |
-
model_kwargs: A `dict`. A dict for the other inputs of the model function.
|
265 |
-
guidance_type: A `str`. The type of the guidance for sampling.
|
266 |
-
"uncond" or "classifier" or "classifier-free".
|
267 |
-
condition: A pytorch tensor. The condition for the guided sampling.
|
268 |
-
Only used for "classifier" or "classifier-free" guidance type.
|
269 |
-
unconditional_condition: A pytorch tensor. The condition for the unconditional sampling.
|
270 |
-
Only used for "classifier-free" guidance type.
|
271 |
-
guidance_scale: A `float`. The scale for the guided sampling.
|
272 |
-
classifier_fn: A classifier function. Only used for the classifier guidance.
|
273 |
-
classifier_kwargs: A `dict`. A dict for the other inputs of the classifier function.
|
274 |
-
Returns:
|
275 |
-
A noise prediction model that accepts the noised data and the continuous time as the inputs.
|
276 |
-
"""
|
277 |
-
|
278 |
-
model_kwargs = model_kwargs or {}
|
279 |
-
classifier_kwargs = classifier_kwargs or {}
|
280 |
-
|
281 |
-
def get_model_input_time(t_continuous):
|
282 |
-
"""
|
283 |
-
Convert the continuous-time `t_continuous` (in [epsilon, T]) to the model input time.
|
284 |
-
For discrete-time DPMs, we convert `t_continuous` in [1 / N, 1] to `t_input` in [0, 1000 * (N - 1) / N].
|
285 |
-
For continuous-time DPMs, we just use `t_continuous`.
|
286 |
-
"""
|
287 |
-
if noise_schedule.schedule == 'discrete':
|
288 |
-
return (t_continuous - 1. / noise_schedule.total_N) * 1000.
|
289 |
-
else:
|
290 |
-
return t_continuous
|
291 |
-
|
292 |
-
def noise_pred_fn(x, t_continuous, cond=None):
|
293 |
-
if t_continuous.reshape((-1,)).shape[0] == 1:
|
294 |
-
t_continuous = t_continuous.expand((x.shape[0]))
|
295 |
-
t_input = get_model_input_time(t_continuous)
|
296 |
-
if cond is None:
|
297 |
-
output = model(x, t_input, None, **model_kwargs)
|
298 |
-
else:
|
299 |
-
output = model(x, t_input, cond, **model_kwargs)
|
300 |
-
if model_type == "noise":
|
301 |
-
return output
|
302 |
-
elif model_type == "x_start":
|
303 |
-
alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous)
|
304 |
-
dims = x.dim()
|
305 |
-
return (x - expand_dims(alpha_t, dims) * output) / expand_dims(sigma_t, dims)
|
306 |
-
elif model_type == "v":
|
307 |
-
alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous)
|
308 |
-
dims = x.dim()
|
309 |
-
return expand_dims(alpha_t, dims) * output + expand_dims(sigma_t, dims) * x
|
310 |
-
elif model_type == "score":
|
311 |
-
sigma_t = noise_schedule.marginal_std(t_continuous)
|
312 |
-
dims = x.dim()
|
313 |
-
return -expand_dims(sigma_t, dims) * output
|
314 |
-
|
315 |
-
def cond_grad_fn(x, t_input, condition):
|
316 |
-
"""
|
317 |
-
Compute the gradient of the classifier, i.e. nabla_{x} log p_t(cond | x_t).
|
318 |
-
"""
|
319 |
-
with torch.enable_grad():
|
320 |
-
x_in = x.detach().requires_grad_(True)
|
321 |
-
log_prob = classifier_fn(x_in, t_input, condition, **classifier_kwargs)
|
322 |
-
return torch.autograd.grad(log_prob.sum(), x_in)[0]
|
323 |
-
|
324 |
-
def model_fn(x, t_continuous, condition, unconditional_condition):
|
325 |
-
"""
|
326 |
-
The noise predicition model function that is used for DPM-Solver.
|
327 |
-
"""
|
328 |
-
if t_continuous.reshape((-1,)).shape[0] == 1:
|
329 |
-
t_continuous = t_continuous.expand((x.shape[0]))
|
330 |
-
if guidance_type == "uncond":
|
331 |
-
return noise_pred_fn(x, t_continuous)
|
332 |
-
elif guidance_type == "classifier":
|
333 |
-
assert classifier_fn is not None
|
334 |
-
t_input = get_model_input_time(t_continuous)
|
335 |
-
cond_grad = cond_grad_fn(x, t_input, condition)
|
336 |
-
sigma_t = noise_schedule.marginal_std(t_continuous)
|
337 |
-
noise = noise_pred_fn(x, t_continuous)
|
338 |
-
return noise - guidance_scale * expand_dims(sigma_t, dims=cond_grad.dim()) * cond_grad
|
339 |
-
elif guidance_type == "classifier-free":
|
340 |
-
if guidance_scale == 1. or unconditional_condition is None:
|
341 |
-
return noise_pred_fn(x, t_continuous, cond=condition)
|
342 |
-
else:
|
343 |
-
x_in = torch.cat([x] * 2)
|
344 |
-
t_in = torch.cat([t_continuous] * 2)
|
345 |
-
if isinstance(condition, dict):
|
346 |
-
assert isinstance(unconditional_condition, dict)
|
347 |
-
c_in = {}
|
348 |
-
for k in condition:
|
349 |
-
if isinstance(condition[k], list):
|
350 |
-
c_in[k] = [torch.cat([
|
351 |
-
unconditional_condition[k][i],
|
352 |
-
condition[k][i]]) for i in range(len(condition[k]))]
|
353 |
-
else:
|
354 |
-
c_in[k] = torch.cat([
|
355 |
-
unconditional_condition[k],
|
356 |
-
condition[k]])
|
357 |
-
elif isinstance(condition, list):
|
358 |
-
c_in = []
|
359 |
-
assert isinstance(unconditional_condition, list)
|
360 |
-
for i in range(len(condition)):
|
361 |
-
c_in.append(torch.cat([unconditional_condition[i], condition[i]]))
|
362 |
-
else:
|
363 |
-
c_in = torch.cat([unconditional_condition, condition])
|
364 |
-
noise_uncond, noise = noise_pred_fn(x_in, t_in, cond=c_in).chunk(2)
|
365 |
-
return noise_uncond + guidance_scale * (noise - noise_uncond)
|
366 |
-
|
367 |
-
assert model_type in ["noise", "x_start", "v"]
|
368 |
-
assert guidance_type in ["uncond", "classifier", "classifier-free"]
|
369 |
-
return model_fn
|
370 |
-
|
371 |
-
|
372 |
-
class UniPC:
|
373 |
-
def __init__(
|
374 |
-
self,
|
375 |
-
model_fn,
|
376 |
-
noise_schedule,
|
377 |
-
predict_x0=True,
|
378 |
-
thresholding=False,
|
379 |
-
max_val=1.,
|
380 |
-
variant='bh1',
|
381 |
-
condition=None,
|
382 |
-
unconditional_condition=None,
|
383 |
-
before_sample=None,
|
384 |
-
after_sample=None,
|
385 |
-
after_update=None
|
386 |
-
):
|
387 |
-
"""Construct a UniPC.
|
388 |
-
|
389 |
-
We support both data_prediction and noise_prediction.
|
390 |
-
"""
|
391 |
-
self.model_fn_ = model_fn
|
392 |
-
self.noise_schedule = noise_schedule
|
393 |
-
self.variant = variant
|
394 |
-
self.predict_x0 = predict_x0
|
395 |
-
self.thresholding = thresholding
|
396 |
-
self.max_val = max_val
|
397 |
-
self.condition = condition
|
398 |
-
self.unconditional_condition = unconditional_condition
|
399 |
-
self.before_sample = before_sample
|
400 |
-
self.after_sample = after_sample
|
401 |
-
self.after_update = after_update
|
402 |
-
|
403 |
-
def dynamic_thresholding_fn(self, x0, t=None):
|
404 |
-
"""
|
405 |
-
The dynamic thresholding method.
|
406 |
-
"""
|
407 |
-
dims = x0.dim()
|
408 |
-
p = self.dynamic_thresholding_ratio
|
409 |
-
s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1)
|
410 |
-
s = expand_dims(torch.maximum(s, self.thresholding_max_val * torch.ones_like(s).to(s.device)), dims)
|
411 |
-
x0 = torch.clamp(x0, -s, s) / s
|
412 |
-
return x0
|
413 |
-
|
414 |
-
def model(self, x, t):
|
415 |
-
cond = self.condition
|
416 |
-
uncond = self.unconditional_condition
|
417 |
-
if self.before_sample is not None:
|
418 |
-
x, t, cond, uncond = self.before_sample(x, t, cond, uncond)
|
419 |
-
res = self.model_fn_(x, t, cond, uncond)
|
420 |
-
if self.after_sample is not None:
|
421 |
-
x, t, cond, uncond, res = self.after_sample(x, t, cond, uncond, res)
|
422 |
-
|
423 |
-
if isinstance(res, tuple):
|
424 |
-
# (None, pred_x0)
|
425 |
-
res = res[1]
|
426 |
-
|
427 |
-
return res
|
428 |
-
|
429 |
-
def noise_prediction_fn(self, x, t):
|
430 |
-
"""
|
431 |
-
Return the noise prediction model.
|
432 |
-
"""
|
433 |
-
return self.model(x, t)
|
434 |
-
|
435 |
-
def data_prediction_fn(self, x, t):
|
436 |
-
"""
|
437 |
-
Return the data prediction model (with thresholding).
|
438 |
-
"""
|
439 |
-
noise = self.noise_prediction_fn(x, t)
|
440 |
-
dims = x.dim()
|
441 |
-
alpha_t, sigma_t = self.noise_schedule.marginal_alpha(t), self.noise_schedule.marginal_std(t)
|
442 |
-
x0 = (x - expand_dims(sigma_t, dims) * noise) / expand_dims(alpha_t, dims)
|
443 |
-
if self.thresholding:
|
444 |
-
p = 0.995 # A hyperparameter in the paper of "Imagen" [1].
|
445 |
-
s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1)
|
446 |
-
s = expand_dims(torch.maximum(s, self.max_val * torch.ones_like(s).to(s.device)), dims)
|
447 |
-
x0 = torch.clamp(x0, -s, s) / s
|
448 |
-
return x0
|
449 |
-
|
450 |
-
def model_fn(self, x, t):
|
451 |
-
"""
|
452 |
-
Convert the model to the noise prediction model or the data prediction model.
|
453 |
-
"""
|
454 |
-
if self.predict_x0:
|
455 |
-
return self.data_prediction_fn(x, t)
|
456 |
-
else:
|
457 |
-
return self.noise_prediction_fn(x, t)
|
458 |
-
|
459 |
-
def get_time_steps(self, skip_type, t_T, t_0, N, device):
|
460 |
-
"""Compute the intermediate time steps for sampling.
|
461 |
-
"""
|
462 |
-
if skip_type == 'logSNR':
|
463 |
-
lambda_T = self.noise_schedule.marginal_lambda(torch.tensor(t_T).to(device))
|
464 |
-
lambda_0 = self.noise_schedule.marginal_lambda(torch.tensor(t_0).to(device))
|
465 |
-
logSNR_steps = torch.linspace(lambda_T.cpu().item(), lambda_0.cpu().item(), N + 1).to(device)
|
466 |
-
return self.noise_schedule.inverse_lambda(logSNR_steps)
|
467 |
-
elif skip_type == 'time_uniform':
|
468 |
-
return torch.linspace(t_T, t_0, N + 1).to(device)
|
469 |
-
elif skip_type == 'time_quadratic':
|
470 |
-
t_order = 2
|
471 |
-
t = torch.linspace(t_T**(1. / t_order), t_0**(1. / t_order), N + 1).pow(t_order).to(device)
|
472 |
-
return t
|
473 |
-
else:
|
474 |
-
raise ValueError(f"Unsupported skip_type {skip_type}, need to be 'logSNR' or 'time_uniform' or 'time_quadratic'")
|
475 |
-
|
476 |
-
def get_orders_and_timesteps_for_singlestep_solver(self, steps, order, skip_type, t_T, t_0, device):
|
477 |
-
"""
|
478 |
-
Get the order of each step for sampling by the singlestep DPM-Solver.
|
479 |
-
"""
|
480 |
-
if order == 3:
|
481 |
-
K = steps // 3 + 1
|
482 |
-
if steps % 3 == 0:
|
483 |
-
orders = [3,] * (K - 2) + [2, 1]
|
484 |
-
elif steps % 3 == 1:
|
485 |
-
orders = [3,] * (K - 1) + [1]
|
486 |
-
else:
|
487 |
-
orders = [3,] * (K - 1) + [2]
|
488 |
-
elif order == 2:
|
489 |
-
if steps % 2 == 0:
|
490 |
-
K = steps // 2
|
491 |
-
orders = [2,] * K
|
492 |
-
else:
|
493 |
-
K = steps // 2 + 1
|
494 |
-
orders = [2,] * (K - 1) + [1]
|
495 |
-
elif order == 1:
|
496 |
-
K = steps
|
497 |
-
orders = [1,] * steps
|
498 |
-
else:
|
499 |
-
raise ValueError("'order' must be '1' or '2' or '3'.")
|
500 |
-
if skip_type == 'logSNR':
|
501 |
-
# To reproduce the results in DPM-Solver paper
|
502 |
-
timesteps_outer = self.get_time_steps(skip_type, t_T, t_0, K, device)
|
503 |
-
else:
|
504 |
-
timesteps_outer = self.get_time_steps(skip_type, t_T, t_0, steps, device)[torch.cumsum(torch.tensor([0,] + orders), 0).to(device)]
|
505 |
-
return timesteps_outer, orders
|
506 |
-
|
507 |
-
def denoise_to_zero_fn(self, x, s):
|
508 |
-
"""
|
509 |
-
Denoise at the final step, which is equivalent to solve the ODE from lambda_s to infty by first-order discretization.
|
510 |
-
"""
|
511 |
-
return self.data_prediction_fn(x, s)
|
512 |
-
|
513 |
-
def multistep_uni_pc_update(self, x, model_prev_list, t_prev_list, t, order, **kwargs):
|
514 |
-
if len(t.shape) == 0:
|
515 |
-
t = t.view(-1)
|
516 |
-
if 'bh' in self.variant:
|
517 |
-
return self.multistep_uni_pc_bh_update(x, model_prev_list, t_prev_list, t, order, **kwargs)
|
518 |
-
else:
|
519 |
-
assert self.variant == 'vary_coeff'
|
520 |
-
return self.multistep_uni_pc_vary_update(x, model_prev_list, t_prev_list, t, order, **kwargs)
|
521 |
-
|
522 |
-
def multistep_uni_pc_vary_update(self, x, model_prev_list, t_prev_list, t, order, use_corrector=True):
|
523 |
-
#print(f'using unified predictor-corrector with order {order} (solver type: vary coeff)')
|
524 |
-
ns = self.noise_schedule
|
525 |
-
assert order <= len(model_prev_list)
|
526 |
-
|
527 |
-
# first compute rks
|
528 |
-
t_prev_0 = t_prev_list[-1]
|
529 |
-
lambda_prev_0 = ns.marginal_lambda(t_prev_0)
|
530 |
-
lambda_t = ns.marginal_lambda(t)
|
531 |
-
model_prev_0 = model_prev_list[-1]
|
532 |
-
sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t)
|
533 |
-
log_alpha_t = ns.marginal_log_mean_coeff(t)
|
534 |
-
alpha_t = torch.exp(log_alpha_t)
|
535 |
-
|
536 |
-
h = lambda_t - lambda_prev_0
|
537 |
-
|
538 |
-
rks = []
|
539 |
-
D1s = []
|
540 |
-
for i in range(1, order):
|
541 |
-
t_prev_i = t_prev_list[-(i + 1)]
|
542 |
-
model_prev_i = model_prev_list[-(i + 1)]
|
543 |
-
lambda_prev_i = ns.marginal_lambda(t_prev_i)
|
544 |
-
rk = (lambda_prev_i - lambda_prev_0) / h
|
545 |
-
rks.append(rk)
|
546 |
-
D1s.append((model_prev_i - model_prev_0) / rk)
|
547 |
-
|
548 |
-
rks.append(1.)
|
549 |
-
rks = torch.tensor(rks, device=x.device)
|
550 |
-
|
551 |
-
K = len(rks)
|
552 |
-
# build C matrix
|
553 |
-
C = []
|
554 |
-
|
555 |
-
col = torch.ones_like(rks)
|
556 |
-
for k in range(1, K + 1):
|
557 |
-
C.append(col)
|
558 |
-
col = col * rks / (k + 1)
|
559 |
-
C = torch.stack(C, dim=1)
|
560 |
-
|
561 |
-
if len(D1s) > 0:
|
562 |
-
D1s = torch.stack(D1s, dim=1) # (B, K)
|
563 |
-
C_inv_p = torch.linalg.inv(C[:-1, :-1])
|
564 |
-
A_p = C_inv_p
|
565 |
-
|
566 |
-
if use_corrector:
|
567 |
-
#print('using corrector')
|
568 |
-
C_inv = torch.linalg.inv(C)
|
569 |
-
A_c = C_inv
|
570 |
-
|
571 |
-
hh = -h if self.predict_x0 else h
|
572 |
-
h_phi_1 = torch.expm1(hh)
|
573 |
-
h_phi_ks = []
|
574 |
-
factorial_k = 1
|
575 |
-
h_phi_k = h_phi_1
|
576 |
-
for k in range(1, K + 2):
|
577 |
-
h_phi_ks.append(h_phi_k)
|
578 |
-
h_phi_k = h_phi_k / hh - 1 / factorial_k
|
579 |
-
factorial_k *= (k + 1)
|
580 |
-
|
581 |
-
model_t = None
|
582 |
-
if self.predict_x0:
|
583 |
-
x_t_ = (
|
584 |
-
sigma_t / sigma_prev_0 * x
|
585 |
-
- alpha_t * h_phi_1 * model_prev_0
|
586 |
-
)
|
587 |
-
# now predictor
|
588 |
-
x_t = x_t_
|
589 |
-
if len(D1s) > 0:
|
590 |
-
# compute the residuals for predictor
|
591 |
-
for k in range(K - 1):
|
592 |
-
x_t = x_t - alpha_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_p[k])
|
593 |
-
# now corrector
|
594 |
-
if use_corrector:
|
595 |
-
model_t = self.model_fn(x_t, t)
|
596 |
-
D1_t = (model_t - model_prev_0)
|
597 |
-
x_t = x_t_
|
598 |
-
k = 0
|
599 |
-
for k in range(K - 1):
|
600 |
-
x_t = x_t - alpha_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_c[k][:-1])
|
601 |
-
x_t = x_t - alpha_t * h_phi_ks[K] * (D1_t * A_c[k][-1])
|
602 |
-
else:
|
603 |
-
log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t)
|
604 |
-
x_t_ = (
|
605 |
-
(torch.exp(log_alpha_t - log_alpha_prev_0)) * x
|
606 |
-
- (sigma_t * h_phi_1) * model_prev_0
|
607 |
-
)
|
608 |
-
# now predictor
|
609 |
-
x_t = x_t_
|
610 |
-
if len(D1s) > 0:
|
611 |
-
# compute the residuals for predictor
|
612 |
-
for k in range(K - 1):
|
613 |
-
x_t = x_t - sigma_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_p[k])
|
614 |
-
# now corrector
|
615 |
-
if use_corrector:
|
616 |
-
model_t = self.model_fn(x_t, t)
|
617 |
-
D1_t = (model_t - model_prev_0)
|
618 |
-
x_t = x_t_
|
619 |
-
k = 0
|
620 |
-
for k in range(K - 1):
|
621 |
-
x_t = x_t - sigma_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_c[k][:-1])
|
622 |
-
x_t = x_t - sigma_t * h_phi_ks[K] * (D1_t * A_c[k][-1])
|
623 |
-
return x_t, model_t
|
624 |
-
|
625 |
-
def multistep_uni_pc_bh_update(self, x, model_prev_list, t_prev_list, t, order, x_t=None, use_corrector=True):
|
626 |
-
#print(f'using unified predictor-corrector with order {order} (solver type: B(h))')
|
627 |
-
ns = self.noise_schedule
|
628 |
-
assert order <= len(model_prev_list)
|
629 |
-
dims = x.dim()
|
630 |
-
|
631 |
-
# first compute rks
|
632 |
-
t_prev_0 = t_prev_list[-1]
|
633 |
-
lambda_prev_0 = ns.marginal_lambda(t_prev_0)
|
634 |
-
lambda_t = ns.marginal_lambda(t)
|
635 |
-
model_prev_0 = model_prev_list[-1]
|
636 |
-
sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t)
|
637 |
-
log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t)
|
638 |
-
alpha_t = torch.exp(log_alpha_t)
|
639 |
-
|
640 |
-
h = lambda_t - lambda_prev_0
|
641 |
-
|
642 |
-
rks = []
|
643 |
-
D1s = []
|
644 |
-
for i in range(1, order):
|
645 |
-
t_prev_i = t_prev_list[-(i + 1)]
|
646 |
-
model_prev_i = model_prev_list[-(i + 1)]
|
647 |
-
lambda_prev_i = ns.marginal_lambda(t_prev_i)
|
648 |
-
rk = ((lambda_prev_i - lambda_prev_0) / h)[0]
|
649 |
-
rks.append(rk)
|
650 |
-
D1s.append((model_prev_i - model_prev_0) / rk)
|
651 |
-
|
652 |
-
rks.append(1.)
|
653 |
-
rks = torch.tensor(rks, device=x.device)
|
654 |
-
|
655 |
-
R = []
|
656 |
-
b = []
|
657 |
-
|
658 |
-
hh = -h[0] if self.predict_x0 else h[0]
|
659 |
-
h_phi_1 = torch.expm1(hh) # h\phi_1(h) = e^h - 1
|
660 |
-
h_phi_k = h_phi_1 / hh - 1
|
661 |
-
|
662 |
-
factorial_i = 1
|
663 |
-
|
664 |
-
if self.variant == 'bh1':
|
665 |
-
B_h = hh
|
666 |
-
elif self.variant == 'bh2':
|
667 |
-
B_h = torch.expm1(hh)
|
668 |
-
else:
|
669 |
-
raise NotImplementedError()
|
670 |
-
|
671 |
-
for i in range(1, order + 1):
|
672 |
-
R.append(torch.pow(rks, i - 1))
|
673 |
-
b.append(h_phi_k * factorial_i / B_h)
|
674 |
-
factorial_i *= (i + 1)
|
675 |
-
h_phi_k = h_phi_k / hh - 1 / factorial_i
|
676 |
-
|
677 |
-
R = torch.stack(R)
|
678 |
-
b = torch.tensor(b, device=x.device)
|
679 |
-
|
680 |
-
# now predictor
|
681 |
-
use_predictor = len(D1s) > 0 and x_t is None
|
682 |
-
if len(D1s) > 0:
|
683 |
-
D1s = torch.stack(D1s, dim=1) # (B, K)
|
684 |
-
if x_t is None:
|
685 |
-
# for order 2, we use a simplified version
|
686 |
-
if order == 2:
|
687 |
-
rhos_p = torch.tensor([0.5], device=b.device)
|
688 |
-
else:
|
689 |
-
rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1])
|
690 |
-
else:
|
691 |
-
D1s = None
|
692 |
-
|
693 |
-
if use_corrector:
|
694 |
-
#print('using corrector')
|
695 |
-
# for order 1, we use a simplified version
|
696 |
-
if order == 1:
|
697 |
-
rhos_c = torch.tensor([0.5], device=b.device)
|
698 |
-
else:
|
699 |
-
rhos_c = torch.linalg.solve(R, b)
|
700 |
-
|
701 |
-
model_t = None
|
702 |
-
if self.predict_x0:
|
703 |
-
x_t_ = (
|
704 |
-
expand_dims(sigma_t / sigma_prev_0, dims) * x
|
705 |
-
- expand_dims(alpha_t * h_phi_1, dims)* model_prev_0
|
706 |
-
)
|
707 |
-
|
708 |
-
if x_t is None:
|
709 |
-
if use_predictor:
|
710 |
-
pred_res = torch.einsum('k,bkchw->bchw', rhos_p, D1s)
|
711 |
-
else:
|
712 |
-
pred_res = 0
|
713 |
-
x_t = x_t_ - expand_dims(alpha_t * B_h, dims) * pred_res
|
714 |
-
|
715 |
-
if use_corrector:
|
716 |
-
model_t = self.model_fn(x_t, t)
|
717 |
-
if D1s is not None:
|
718 |
-
corr_res = torch.einsum('k,bkchw->bchw', rhos_c[:-1], D1s)
|
719 |
-
else:
|
720 |
-
corr_res = 0
|
721 |
-
D1_t = (model_t - model_prev_0)
|
722 |
-
x_t = x_t_ - expand_dims(alpha_t * B_h, dims) * (corr_res + rhos_c[-1] * D1_t)
|
723 |
-
else:
|
724 |
-
x_t_ = (
|
725 |
-
expand_dims(torch.exp(log_alpha_t - log_alpha_prev_0), dims) * x
|
726 |
-
- expand_dims(sigma_t * h_phi_1, dims) * model_prev_0
|
727 |
-
)
|
728 |
-
if x_t is None:
|
729 |
-
if use_predictor:
|
730 |
-
pred_res = torch.einsum('k,bkchw->bchw', rhos_p, D1s)
|
731 |
-
else:
|
732 |
-
pred_res = 0
|
733 |
-
x_t = x_t_ - expand_dims(sigma_t * B_h, dims) * pred_res
|
734 |
-
|
735 |
-
if use_corrector:
|
736 |
-
model_t = self.model_fn(x_t, t)
|
737 |
-
if D1s is not None:
|
738 |
-
corr_res = torch.einsum('k,bkchw->bchw', rhos_c[:-1], D1s)
|
739 |
-
else:
|
740 |
-
corr_res = 0
|
741 |
-
D1_t = (model_t - model_prev_0)
|
742 |
-
x_t = x_t_ - expand_dims(sigma_t * B_h, dims) * (corr_res + rhos_c[-1] * D1_t)
|
743 |
-
return x_t, model_t
|
744 |
-
|
745 |
-
|
746 |
-
def sample(self, x, steps=20, t_start=None, t_end=None, order=3, skip_type='time_uniform',
|
747 |
-
method='singlestep', lower_order_final=True, denoise_to_zero=False, solver_type='dpm_solver',
|
748 |
-
atol=0.0078, rtol=0.05, corrector=False,
|
749 |
-
):
|
750 |
-
t_0 = 1. / self.noise_schedule.total_N if t_end is None else t_end
|
751 |
-
t_T = self.noise_schedule.T if t_start is None else t_start
|
752 |
-
device = x.device
|
753 |
-
if method == 'multistep':
|
754 |
-
assert steps >= order, "UniPC order must be < sampling steps"
|
755 |
-
timesteps = self.get_time_steps(skip_type=skip_type, t_T=t_T, t_0=t_0, N=steps, device=device)
|
756 |
-
#print(f"Running UniPC Sampling with {timesteps.shape[0]} timesteps, order {order}")
|
757 |
-
assert timesteps.shape[0] - 1 == steps
|
758 |
-
with torch.no_grad():
|
759 |
-
vec_t = timesteps[0].expand((x.shape[0]))
|
760 |
-
model_prev_list = [self.model_fn(x, vec_t)]
|
761 |
-
t_prev_list = [vec_t]
|
762 |
-
with tqdm.tqdm(total=steps) as pbar:
|
763 |
-
# Init the first `order` values by lower order multistep DPM-Solver.
|
764 |
-
for init_order in range(1, order):
|
765 |
-
vec_t = timesteps[init_order].expand(x.shape[0])
|
766 |
-
x, model_x = self.multistep_uni_pc_update(x, model_prev_list, t_prev_list, vec_t, init_order, use_corrector=True)
|
767 |
-
if model_x is None:
|
768 |
-
model_x = self.model_fn(x, vec_t)
|
769 |
-
if self.after_update is not None:
|
770 |
-
self.after_update(x, model_x)
|
771 |
-
model_prev_list.append(model_x)
|
772 |
-
t_prev_list.append(vec_t)
|
773 |
-
pbar.update()
|
774 |
-
|
775 |
-
for step in range(order, steps + 1):
|
776 |
-
vec_t = timesteps[step].expand(x.shape[0])
|
777 |
-
if lower_order_final:
|
778 |
-
step_order = min(order, steps + 1 - step)
|
779 |
-
else:
|
780 |
-
step_order = order
|
781 |
-
#print('this step order:', step_order)
|
782 |
-
if step == steps:
|
783 |
-
#print('do not run corrector at the last step')
|
784 |
-
use_corrector = False
|
785 |
-
else:
|
786 |
-
use_corrector = True
|
787 |
-
x, model_x = self.multistep_uni_pc_update(x, model_prev_list, t_prev_list, vec_t, step_order, use_corrector=use_corrector)
|
788 |
-
if self.after_update is not None:
|
789 |
-
self.after_update(x, model_x)
|
790 |
-
for i in range(order - 1):
|
791 |
-
t_prev_list[i] = t_prev_list[i + 1]
|
792 |
-
model_prev_list[i] = model_prev_list[i + 1]
|
793 |
-
t_prev_list[-1] = vec_t
|
794 |
-
# We do not need to evaluate the final model value.
|
795 |
-
if step < steps:
|
796 |
-
if model_x is None:
|
797 |
-
model_x = self.model_fn(x, vec_t)
|
798 |
-
model_prev_list[-1] = model_x
|
799 |
-
pbar.update()
|
800 |
-
else:
|
801 |
-
raise NotImplementedError()
|
802 |
-
if denoise_to_zero:
|
803 |
-
x = self.denoise_to_zero_fn(x, torch.ones((x.shape[0],)).to(device) * t_0)
|
804 |
-
return x
|
805 |
-
|
806 |
-
|
807 |
-
#############################################################
|
808 |
-
# other utility functions
|
809 |
-
#############################################################
|
810 |
-
|
811 |
-
def interpolate_fn(x, xp, yp):
|
812 |
-
"""
|
813 |
-
A piecewise linear function y = f(x), using xp and yp as keypoints.
|
814 |
-
We implement f(x) in a differentiable way (i.e. applicable for autograd).
|
815 |
-
The function f(x) is well-defined for all x-axis. (For x beyond the bounds of xp, we use the outmost points of xp to define the linear function.)
|
816 |
-
|
817 |
-
Args:
|
818 |
-
x: PyTorch tensor with shape [N, C], where N is the batch size, C is the number of channels (we use C = 1 for DPM-Solver).
|
819 |
-
xp: PyTorch tensor with shape [C, K], where K is the number of keypoints.
|
820 |
-
yp: PyTorch tensor with shape [C, K].
|
821 |
-
Returns:
|
822 |
-
The function values f(x), with shape [N, C].
|
823 |
-
"""
|
824 |
-
N, K = x.shape[0], xp.shape[1]
|
825 |
-
all_x = torch.cat([x.unsqueeze(2), xp.unsqueeze(0).repeat((N, 1, 1))], dim=2)
|
826 |
-
sorted_all_x, x_indices = torch.sort(all_x, dim=2)
|
827 |
-
x_idx = torch.argmin(x_indices, dim=2)
|
828 |
-
cand_start_idx = x_idx - 1
|
829 |
-
start_idx = torch.where(
|
830 |
-
torch.eq(x_idx, 0),
|
831 |
-
torch.tensor(1, device=x.device),
|
832 |
-
torch.where(
|
833 |
-
torch.eq(x_idx, K), torch.tensor(K - 2, device=x.device), cand_start_idx,
|
834 |
-
),
|
835 |
-
)
|
836 |
-
end_idx = torch.where(torch.eq(start_idx, cand_start_idx), start_idx + 2, start_idx + 1)
|
837 |
-
start_x = torch.gather(sorted_all_x, dim=2, index=start_idx.unsqueeze(2)).squeeze(2)
|
838 |
-
end_x = torch.gather(sorted_all_x, dim=2, index=end_idx.unsqueeze(2)).squeeze(2)
|
839 |
-
start_idx2 = torch.where(
|
840 |
-
torch.eq(x_idx, 0),
|
841 |
-
torch.tensor(0, device=x.device),
|
842 |
-
torch.where(
|
843 |
-
torch.eq(x_idx, K), torch.tensor(K - 2, device=x.device), cand_start_idx,
|
844 |
-
),
|
845 |
-
)
|
846 |
-
y_positions_expanded = yp.unsqueeze(0).expand(N, -1, -1)
|
847 |
-
start_y = torch.gather(y_positions_expanded, dim=2, index=start_idx2.unsqueeze(2)).squeeze(2)
|
848 |
-
end_y = torch.gather(y_positions_expanded, dim=2, index=(start_idx2 + 1).unsqueeze(2)).squeeze(2)
|
849 |
-
cand = start_y + (x - start_x) * (end_y - start_y) / (end_x - start_x)
|
850 |
-
return cand
|
851 |
-
|
852 |
-
|
853 |
-
def expand_dims(v, dims):
|
854 |
-
"""
|
855 |
-
Expand the tensor `v` to the dim `dims`.
|
856 |
-
|
857 |
-
Args:
|
858 |
-
`v`: a PyTorch tensor with shape [N].
|
859 |
-
`dim`: a `int`.
|
860 |
-
Returns:
|
861 |
-
a PyTorch tensor with shape [N, 1, 1, ..., 1] and the total dimension is `dims`.
|
862 |
-
"""
|
863 |
-
return v[(...,) + (None,)*(dims - 1)]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|