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sampler_rk.py
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sampler_rk.py
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import torch
import torch.nn.functional as F
import torchvision.transforms as T
from tqdm.auto import trange
import math
import copy
import gc
import comfy.model_patcher
from .noise_classes import *
from .extra_samplers_helpers import get_deis_coeff_list
from .noise_sigmas_timesteps_scaling import get_res4lyf_step_with_model, get_res4lyf_half_step3
from .latents import hard_light_blend
def get_epsilon(model, x, sigma, **extra_args):
s_in = x.new_ones([x.shape[0]])
x0 = model(x, sigma * s_in, **extra_args)
eps = (x - x0) / (sigma * s_in)
return eps
def get_denoised(model, x, sigma, **extra_args):
s_in = x.new_ones([x.shape[0]])
x0 = model(x, sigma * s_in, **extra_args)
return x0
def __phi(j, neg_h):
remainder = torch.zeros_like(neg_h)
for k in range(j):
remainder += (neg_h)**k / math.factorial(k)
phi_j_h = ((neg_h).exp() - remainder) / (neg_h)**j
return phi_j_h
def calculate_gamma(c2, c3):
return (3*(c3**3) - 2*c3) / (c2*(2 - 3*c2))
from typing import Protocol, Optional, Dict, Any, TypedDict, NamedTuple
def _gamma(n: int,) -> int:
"""
https://en.wikipedia.org/wiki/Gamma_function
for every positive integer n,
Γ(n) = (n-1)!
"""
return math.factorial(n-1)
def _incomplete_gamma(s: int, x: float, gamma_s: Optional[int] = None) -> float:
"""
https://en.wikipedia.org/wiki/Incomplete_gamma_function#Special_values
if s is a positive integer,
Γ(s, x) = (s-1)!*∑{k=0..s-1}(x^k/k!)
"""
if gamma_s is None:
gamma_s = _gamma(s)
sum_: float = 0
# {k=0..s-1} inclusive
for k in range(s):
numerator: float = x**k
denom: int = math.factorial(k)
quotient: float = numerator/denom
sum_ += quotient
incomplete_gamma_: float = sum_ * math.exp(-x) * gamma_s
return incomplete_gamma_
def phi(j: int, neg_h: float, ):
"""
For j={1,2,3}: you could alternatively use Kat's phi_1, phi_2, phi_3 which perform fewer steps
Lemma 1
https://arxiv.org/abs/2308.02157
ϕj(-h) = 1/h^j*∫{0..h}(e^(τ-h)*(τ^(j-1))/((j-1)!)dτ)
https://www.wolframalpha.com/input?i=integrate+e%5E%28%CF%84-h%29*%28%CF%84%5E%28j-1%29%2F%28j-1%29%21%29d%CF%84
= 1/h^j*[(e^(-h)*(-τ)^(-j)*τ(j))/((j-1)!)]{0..h}
https://www.wolframalpha.com/input?i=integrate+e%5E%28%CF%84-h%29*%28%CF%84%5E%28j-1%29%2F%28j-1%29%21%29d%CF%84+between+0+and+h
= 1/h^j*((e^(-h)*(-h)^(-j)*h^j*(Γ(j)-Γ(j,-h)))/(j-1)!)
= (e^(-h)*(-h)^(-j)*h^j*(Γ(j)-Γ(j,-h))/((j-1)!*h^j)
= (e^(-h)*(-h)^(-j)*(Γ(j)-Γ(j,-h))/(j-1)!
= (e^(-h)*(-h)^(-j)*(Γ(j)-Γ(j,-h))/Γ(j)
= (e^(-h)*(-h)^(-j)*(1-Γ(j,-h)/Γ(j))
requires j>0
"""
assert j > 0
gamma_: float = _gamma(j)
incomp_gamma_: float = _incomplete_gamma(j, neg_h, gamma_s=gamma_)
phi_: float = math.exp(neg_h) * neg_h**-j * (1-incomp_gamma_/gamma_)
return phi_
rk_coeff = {
"gauss-legendre_5s": (
[
[4563950663 / 32115191526,
(310937500000000 / 2597974476091533 + 45156250000 * (739**0.5) / 8747388808389),
(310937500000000 / 2597974476091533 - 45156250000 * (739**0.5) / 8747388808389),
(5236016175 / 88357462711 + 709703235 * (739**0.5) / 353429850844),
(5236016175 / 88357462711 - 709703235 * (739**0.5) / 353429850844)],
[(4563950663 / 32115191526 - 38339103 * (739**0.5) / 6250000000),
(310937500000000 / 2597974476091533 + 9557056475401 * (739**0.5) / 3498955523355600000),
(310937500000000 / 2597974476091533 - 14074198220719489 * (739**0.5) / 3498955523355600000),
(5236016175 / 88357462711 + 5601362553163918341 * (739**0.5) / 2208936567775000000000),
(5236016175 / 88357462711 - 5040458465159165409 * (739**0.5) / 2208936567775000000000)],
[(4563950663 / 32115191526 + 38339103 * (739**0.5) / 6250000000),
(310937500000000 / 2597974476091533 + 14074198220719489 * (739**0.5) / 3498955523355600000),
(310937500000000 / 2597974476091533 - 9557056475401 * (739**0.5) / 3498955523355600000),
(5236016175 / 88357462711 + 5040458465159165409 * (739**0.5) / 2208936567775000000000),
(5236016175 / 88357462711 - 5601362553163918341 * (739**0.5) / 2208936567775000000000)],
[(4563950663 / 32115191526 - 38209 * (739**0.5) / 7938810),
(310937500000000 / 2597974476091533 - 359369071093750 * (739**0.5) / 70145310854471391),
(310937500000000 / 2597974476091533 - 323282178906250 * (739**0.5) / 70145310854471391),
(5236016175 / 88357462711 - 470139 * (739**0.5) / 1413719403376),
(5236016175 / 88357462711 - 44986764863 * (739**0.5) / 21205791050640)],
[(4563950663 / 32115191526 + 38209 * (739**0.5) / 7938810),
(310937500000000 / 2597974476091533 + 359369071093750 * (739**0.5) / 70145310854471391),
(310937500000000 / 2597974476091533 + 323282178906250 * (739**0.5) / 70145310854471391),
(5236016175 / 88357462711 + 44986764863 * (739**0.5) / 21205791050640),
(5236016175 / 88357462711 + 470139 * (739**0.5) / 1413719403376)],
[4563950663 / 16057595763,
621875000000000 / 2597974476091533,
621875000000000 / 2597974476091533,
10472032350 / 88357462711,
10472032350 / 88357462711]
],
[
1 / 2,
1 / 2 - 99 * (739**0.5) / 10000,
1 / 2 + 99 * (739**0.5) / 10000,
1 / 2 - (739**0.5) / 60,
1 / 2 + (739**0.5) / 60
]
),
"gauss-legendre_4s": (
[
[1/4, 1/4 - 15**0.5 / 6, 1/4 + 15**0.5 / 6, 1/4],
[1/4 + 15**0.5 / 6, 1/4, 1/4 - 15**0.5 / 6, 1/4],
[1/4, 1/4 + 15**0.5 / 6, 1/4, 1/4 - 15**0.5 / 6],
[1/4 - 15**0.5 / 6, 1/4, 1/4 + 15**0.5 / 6, 1/4],
[1/8, 3/8, 3/8, 1/8]
],
[
1/2 - 15**0.5 / 10,
1/2 + 15**0.5 / 10,
1/2 + 15**0.5 / 10,
1/2 - 15**0.5 / 10
]
),
"gauss-legendre_3s": (
[
[5/36, 2/9 - 15**0.5 / 15, 5/36 - 15**0.5 / 30],
[5/36 + 15**0.5 / 24, 2/9, 5/36 - 15**0.5 / 24],
[5/36 + 15**0.5 / 30, 2/9 + 15**0.5 / 15, 5/36],
[5/18, 4/9, 5/18]
],
[1/2 - 15**0.5 / 10, 1/2, 1/2 + 15**0.5 / 10]
),
"gauss-legendre_2s": (
[
[1/4, 1/4 - 3**0.5 / 6],
[1/4 + 3**0.5 / 6, 1/4],
[1/2, 1/2],
],
[1/2 - 3**0.5 / 6, 1/2 + 3**0.5 / 6]
),
"radau_iia_3s": (
[
[11/45 - 7*6**0.5 / 360, 37/225 - 169*6**0.5 / 1800, -2/225 + 6**0.5 / 75],
[37/225 + 169*6**0.5 / 1800, 11/45 + 7*6**0.5 / 360, -2/225 - 6**0.5 / 75],
[4/9 - 6**0.5 / 36, 4/9 + 6**0.5 / 36, 1/9],
[4/9 - 6**0.5 / 36, 4/9 + 6**0.5 / 36, 1/9],
],
[2/5 - 6**0.5 / 10, 2/5 + 6**0.5 / 10, 1.]
),
"radau_iia_2s": (
[
[5/12, -1/12],
[3/4, 1/4],
[3/4, 1/4],
],
[1/3, 1]
),
"lobatto_iiic_3s": (
[
[1/6, -1/3, 1/6],
[1/6, 5/12, -1/12],
[1/6, 2/3, 1/6],
[1/6, 2/3, 1/6],
],
[0, 1/2, 1]
),
"lobatto_iiic_2s": (
[
[1/2, -1/2],
[1/2, 1/2],
[1/2, 1/2],
],
[0, 1]
),
"dormand-prince_13s": (
[
[1/18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1/48, 1/16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1/32, 0, 3/32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[5/16, 0, -75/64, 75/64, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[3/80, 0, 0, 3/16, 3/20, 0, 0, 0, 0, 0, 0, 0, 0],
[29443841/614563906, 0, 0, 77736538/692538347, -28693883/1125000000, 23124283/1800000000, 0, 0, 0, 0, 0, 0, 0],
[16016141/946692911, 0, 0, 61564180/158732637, 22789713/633445777, 545815736/2771057229, -180193667/1043307555, 0, 0, 0, 0, 0, 0],
[39632708/573591083, 0, 0, -433636366/683701615, -421739975/2616292301, 100302831/723423059, 790204164/839813087, 800635310/3783071287, 0, 0, 0, 0, 0],
[246121993/1340847787, 0, 0, -37695042795/15268766246, -309121744/1061227803, -12992083/490766935, 6005943493/2108947869, 393006217/1396673457, 123872331/1001029789, 0, 0, 0, 0],
[-1028468189/846180014, 0, 0, 8478235783/508512852, 1311729495/1432422823, -10304129995/1701304382, -48777925059/3047939560, 15336726248/1032824649, -45442868181/3398467696, 3065993473/597172653, 0, 0, 0],
[185892177/718116043, 0, 0, -3185094517/667107341, -477755414/1098053517, -703635378/230739211, 5731566787/1027545527, 5232866602/850066563, -4093664535/808688257, 3962137247/1805957418, 65686358/487910083, 0, 0],
[403863854/491063109, 0, 0, -5068492393/434740067, -411421997/543043805, 652783627/914296604, 11173962825/925320556, -13158990841/6184727034, 3936647629/1978049680, -160528059/685178525, 248638103/1413531060, 0, 0],
[14005451/335480064, 0, 0, 0, 0, -59238493/1068277825, 181606767/758867731, 561292985/797845732, -1041891430/1371343529, 760417239/1151165299, 118820643/751138087, -528747749/2220607170, 1/4]
],
[0, 1/18, 1/12, 1/8, 5/16, 3/8, 59/400, 93/200, 5490023248 / 9719169821, 13/20, 1201146811 / 1299019798, 1, 1],
),
"dormand-prince_6s": (
[
[1/5, 0, 0, 0, 0, 0, 0],
[3/40, 9/40, 0, 0, 0, 0, 0],
[44/45, -56/15, 32/9, 0, 0, 0, 0],
[19372/6561, -25360/2187, 64448/6561, -212/729, 0, 0, 0],
[9017/3168, -355/33, 46732/5247, 49/176, -5103/18656, 0],
[35/384, 0, 500/1113, 125/192, -2187/6784, 11/84, 0],
],
[0, 1/5, 3/10, 4/5, 8/9, 1],
),
"dormand-prince_6s_alt": (
[
[1/5, 0, 0, 0, 0, 0, 0],
[3/40, 9/40, 0, 0, 0, 0, 0],
[44/45, -56/15, 32/9, 0, 0, 0, 0],
[19372/6561, -25360/2187, 64448/6561, -212/729, 0, 0, 0],
[9017/3168, -355/33, 46732/5247, 49/176, -5103/18656, 0],
[35/384, 0, 500/1113, 125/192, -2187/6784, 11/84, 0],
],
[0, 1/5, 3/10, 4/5, 8/9, 1],
),
"dormand-prince_7s": (
[
[1/5, 0, 0, 0, 0, 0, 0],
[3/40, 9/40, 0, 0, 0, 0, 0],
[44/45, -56/15, 32/9, 0, 0, 0, 0],
[19372/6561, -25360/2187, 64448/6561, -212/729, 0, 0, 0],
[9017/3168, -355/33, 46732/5247, 49/176, -5103/18656, 0],
[35/384, 0, 500/1113, 125/192, -2187/6784, 11/84, 0],
],
[0, 1/5, 3/10, 4/5, 8/9, 1],
),
"bogacki-shampine_7s": ( #5th order
[
[1/6, 0, 0, 0, 0, 0, 0],
[2/27, 4/27, 0, 0, 0, 0, 0],
[183/1372, -162/343, 1053/1372, 0, 0, 0, 0],
[68/297, -4/11, 42/143, 1960/3861, 0, 0, 0],
[597/22528, 81/352, 63099/585728, 58653/366080, 4617/20480, 0, 0],
[174197/959244, -30942/79937, 8152137/19744439, 666106/1039181, -29421/29068, 482048/414219, 0],
[587/8064, 0, 4440339/15491840, 24353/124800, 387/44800, 2152/5985, 7267/94080]
],
[0, 1/6, 2/9, 3/7, 2/3, 3/4, 1]
),
"rk4_4s": (
[
[1/2, 0, 0, 0],
[0, 1/2, 0, 0],
[0, 0, 1, 0],
[1/6, 1/3, 1/3, 1/6]
],
[0, 1/2, 1/2, 1],
),
"rk38_4s": (
[
[1/3, 0, 0, 0],
[-1/3, 1, 0, 0],
[1, -1, 1, 0],
[1/8, 3/8, 3/8, 1/8]
],
[0, 1/3, 2/3, 1],
),
"ralston_4s": (
[
[2/5, 0, 0, 0],
[(-2889+1428 * 5**0.5)/1024, (3785-1620 * 5**0.5)/1024, 0, 0],
[(-3365+2094 * 5**0.5)/6040, (-975-3046 * 5**0.5)/2552, (467040+203968*5**0.5)/240845, 0],
[(263+24*5**0.5)/1812, (125-1000*5**0.5)/3828, (3426304+1661952*5**0.5)/5924787, (30-4*5**0.5)/123]
],
[0, 2/5, (14-3 * 5**0.5)/16, 1],
),
"heun_3s": (
[
[1/3, 0, 0],
[0, 2/3, 0],
[1/4, 0, 3/4]
],
[0, 1/3, 2/3],
),
"kutta_3s": (
[
[1/2, 0, 0],
[-1, 2, 0],
[1/6, 2/3, 1/6]
],
[0, 1/2, 1],
),
"ralston_3s": (
[
[1/2, 0, 0],
[0, 3/4, 0],
[2/9, 1/3, 4/9]
],
[0, 1/2, 3/4],
),
"houwen-wray_3s": (
[
[8/15, 0, 0],
[1/4, 5/12, 0],
[1/4, 0, 3/4]
],
[0, 8/15, 2/3],
),
"ssprk3_3s": (
[
[1, 0, 0],
[1/4, 1/4, 0],
[1/6, 1/6, 2/3]
],
[0, 1, 1/2],
),
"midpoint_2s": (
[
[1/2, 0],
[0, 1]
],
[0, 1/2],
),
"heun_2s": (
[
[1, 0],
[1/2, 1/2]
],
[0, 1],
),
"ralston_2s": (
[
[2/3, 0],
[1/4, 3/4]
],
[0, 2/3],
),
"euler": (
[
[1],
],
[0],
),
}
def get_rk_methods(rk_type, h, c1=0.0, c2=0.5, c3=1.0, h_prev=None, h_prev2=None, stepcount=0, sigmas=None):
FSAL = False
multistep_stages = 0
if rk_type[:4] == "deis":
order = int(rk_type[-2])
if stepcount < order:
if order == 4:
rk_type = "res_3s"
order = 3
elif order == 3:
rk_type = "res_3s"
elif order == 2:
rk_type = "res_2s"
else:
rk_type = "deis"
multistep_stages = order-1
if rk_type[-2:] == "2m": #multistep method
if h_prev is not None:
multistep_stages = 1
c2 = -h_prev / h
rk_type = rk_type[:-2] + "2s"
else:
rk_type = rk_type[:-2] + "2s"
if rk_type[-2:] == "3m": #multistep method
if h_prev2 is not None:
multistep_stages = 2
c2 = -h_prev2 / h_prev
c3 = -h_prev / h
rk_type = rk_type[:-2] + "3s"
else:
rk_type = rk_type[:-2] + "3s"
if rk_type in rk_coeff:
ab, ci = copy.deepcopy(rk_coeff[rk_type])
ci = ci[:]
ci.append(1)
alpha_fn = lambda h: 1
t_fn = lambda sigma: sigma
sigma_fn = lambda t: t
h_fn = lambda sigma_down, sigma: sigma_down - sigma
model_call = get_denoised
EPS_PRED = False
else:
alpha_fn = lambda neg_h: torch.exp(neg_h)
t_fn = lambda sigma: sigma.log().neg()
sigma_fn = lambda t: t.neg().exp()
h_fn = lambda sigma_down, sigma: -torch.log(sigma_down/sigma)
model_call = get_denoised
EPS_PRED = False
match rk_type:
case "deis":
alpha_fn = lambda neg_h: torch.exp(neg_h)
t_fn = lambda sigma: sigma.log().neg()
sigma_fn = lambda t: t.neg().exp()
h_fn = lambda sigma_down, sigma: -torch.log(sigma_down/sigma)
model_call = get_epsilon
EPS_PRED = True
coeff_list = get_deis_coeff_list(sigmas, multistep_stages+1, deis_mode="rhoab")
coeff_list = [[elem / h for elem in inner_list] for inner_list in coeff_list]
if multistep_stages == 1:
b1, b2 = coeff_list[stepcount]
ab = [
[0, 0],
[b1, b2],
]
ci = [0, 0, 1]
if multistep_stages == 2:
b1, b2, b3 = coeff_list[stepcount]
ab = [
[0, 0, 0],
[0, 0, 0],
[b1, b2, b3],
]
ci = [0, 0, 0, 1]
if multistep_stages == 3:
b1, b2, b3, b4 = coeff_list[stepcount]
ab = [
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[b1, b2, b3, b4],
]
ci = [0, 0, 0, 0, 1]
case "dormand-prince_6s":
FSAL = True
case "ddim":
b1 = phi(1, -h)
ab = [
[b1],
]
ci = [0, 1]
case "res_2s":
a2_1 = c2 * phi(1, -h*c2)
b1 = phi(1, -h) - phi(2, -h)/c2
b2 = phi(2, -h)/c2
a2_1 /= (1 - torch.exp(-h*c2)) / h
b1 /= phi(1, -h)
b2 /= phi(1, -h)
ab = [
[a2_1, 0],
[b1, b2],
]
ci = [0, c2, 1]
case "res_3s":
gamma = calculate_gamma(c2, c3)
a2_1 = c2 * phi(1, -h*c2)
a3_2 = gamma * c2 * phi(2, -h*c2) + (c3 ** 2 / c2) * phi(2, -h*c3) #phi_2_c3_h # a32 from k2 to k3
a3_1 = c3 * phi(1, -h*c3) - a3_2 # a31 from k1 to k3
b3 = (1 / (gamma * c2 + c3)) * phi(2, -h)
b2 = gamma * b3 #simplified version of: b2 = (gamma / (gamma * c2 + c3)) * phi_2_h
b1 = phi(1, -h) - b2 - b3
0
a3_2 /= (1 - torch.exp(-h*c3)) / h
a3_1 /= (1 - torch.exp(-h*c3)) / h
b1 /= phi(1, -h)
b2 /= phi(1, -h)
b3 /= phi(1, -h)
ab = [
[a2_1, 0, 0],
[a3_1, a3_2, 0],
[b1, b2, b3],
]
ci = [c1, c2, c3, 1]
#ci = [0, c2, c3, 1]
case "dpmpp_2s":
#c2 = 0.5
a2_1 = c2 * phi(1, -h*c2)
b1 = (1 - 1/(2*c2)) * phi(1, -h)
b2 = (1/(2*c2)) * phi(1, -h)
a2_1 /= (1 - torch.exp(-h*c2)) / h
b1 /= phi(1, -h)
b2 /= phi(1, -h)
ab = [
[a2_1, 0],
[b1, b2],
]
ci = [0, c2, 1]
case "dpmpp_sde_2s":
c2 = 1.0 #hardcoded to 1.0 to more closely emulate the configuration for k-diffusion's implementation
a2_1 = c2 * phi(1, -h*c2)
b1 = (1 - 1/(2*c2)) * phi(1, -h)
b2 = (1/(2*c2)) * phi(1, -h)
a2_1 /= (1 - torch.exp(-h*c2)) / h
b1 /= phi(1, -h)
b2 /= phi(1, -h)
ab = [
[a2_1, 0],
[b1, b2],
]
ci = [0, c2, 1]
case "dpmpp_3s":
a2_1 = c2 * phi(1, -h*c2)
a3_2 = (c3**2 / c2) * phi(2, -h*c3)
a3_1 = c3 * phi(1, -h*c3) - a3_2
b2 = 0
b3 = (1/c3) * phi(2, -h)
b1 = phi(1, -h) - b2 - b3
a2_1 /= (1 - torch.exp(-h*c2)) / h
a3_2 /= (1 - torch.exp(-h*c3)) / h
a3_1 /= (1 - torch.exp(-h*c3)) / h
b1 /= phi(1, -h)
b2 /= phi(1, -h)
b3 /= phi(1, -h)
ab = [
[a2_1, 0, 0],
[a3_1, a3_2, 0],
[b1, b2, b3],
]
ci = [0, c2, c3, 1]
case "rk_exp_5s":
c1, c2, c3, c4, c5 = 0., 0.5, 0.5, 1., 0.5
a2_1 = 0.5 * phi(1, -h * c2)
a3_1 = 0.5 * phi(1, -h * c3) - phi(2, -h * c3)
a3_2 = phi(2, -h * c3)
a4_1 = phi(1, -h * c4) - 2 * phi(2, -h * c4)
a4_2 = a4_3 = phi(2, -h * c4)
a5_2 = a5_3 = 0.5 * phi(2, -h * c5) - phi(3, -h * c4) + 0.25 * phi(2, -h * c4) - 0.5 * phi(3, -h * c5)
a5_4 = 0.25 * phi(2, -h * c5) - a5_2
a5_1 = 0.5 * phi(1, -h * c5) - 2 * a5_2 - a5_4
b1 = phi(1, -h) - 3 * phi(2, -h) + 4 * phi(3, -h)
b2 = b3 = 0
b4 = -phi(2, -h) + 4*phi(3, -h)
b5 = 4 * phi(2, -h) - 8 * phi(3, -h)
a2_1 /= (1 - torch.exp(-h*c2)) / h
a3_1 /= (1 - torch.exp(-h*c3)) / h
a3_2 /= (1 - torch.exp(-h*c3)) / h
a4_1 /= (1 - torch.exp(-h*c4)) / h
a4_2 /= (1 - torch.exp(-h*c4)) / h
a4_3 /= (1 - torch.exp(-h*c4)) / h
a5_1 /= (1 - torch.exp(-h*c5)) / h
a5_2 /= (1 - torch.exp(-h*c5)) / h
a5_3 /= (1 - torch.exp(-h*c5)) / h
a5_4 /= (1 - torch.exp(-h*c5)) / h
b1 /= phi(1, -h)
b2 /= phi(1, -h)
b3 /= phi(1, -h)
b4 /= phi(1, -h)
b5 /= phi(1, -h)
ab = [
[a2_1, 0, 0, 0, 0],
[a3_1, a3_2, 0, 0, 0],
[a4_1, a4_2, a4_3, 0, 0],
[a5_1, a5_2, a5_3, a5_4, 0],
[b1, b2, b3, b4, b5],
]
ci = [0., 0.5, 0.5, 1., 0.5, 1]
return ab, ci, multistep_stages, model_call, alpha_fn, t_fn, sigma_fn, h_fn, FSAL, EPS_PRED
def get_rk_methods_order(rk_type):
ab, ci, multistep_stages, model_call, alpha_fn, t_fn, sigma_fn, h_fn, FSAL, EPS_PRED = get_rk_methods(rk_type, torch.tensor(1.0).to('cuda').to(torch.float64), c1=0.0, c2=0.5, c3=1.0)
return len(ci)-1
def get_rk_methods_order_and_fn(rk_type, h=None, c1=None, c2=None, c3=None, h_prev=None, h_prev2=None, stepcount=0, sigmas=None):
if h == None:
ab, ci, multistep_stages, model_call, alpha_fn, t_fn, sigma_fn, h_fn, FSAL, EPS_PRED = get_rk_methods(rk_type, torch.tensor(1.0).to('cuda').to(torch.float64), c1=0.0, c2=0.5, c3=1.0)
else:
ab, ci, multistep_stages, model_call, alpha_fn, t_fn, sigma_fn, h_fn, FSAL, EPS_PRED = get_rk_methods(rk_type, h, c1, c2, c3, h_prev, h_prev2, stepcount, sigmas)
return len(ci)-1, model_call, alpha_fn, t_fn, sigma_fn, h_fn, FSAL, EPS_PRED
def get_rk_methods_coeff(rk_type, h, c1, c2, c3, h_prev=None, h_prev2=None, stepcount=0, sigmas=None):
ab, ci, multistep_stages, model_call, alpha_fn, t_fn, sigma_fn, h_fn, FSAL, EPS_PRED = get_rk_methods(rk_type, h, c1, c2, c3, h_prev, h_prev2, stepcount, sigmas)
return ab, ci, multistep_stages, EPS_PRED
@torch.no_grad()
def sample_rk(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None, noise_sampler_type="brownian", noise_mode="hard", noise_seed=-1, rk_type="res_2m", implicit_sampler_name="default",
sigma_fn_formula="", t_fn_formula="",
eta=0.0, eta_var=0.0, s_noise=1., d_noise=1., alpha=-1.0, k=1.0, scale=0.1, c1=0.0, c2=0.5, c3=1.0, MULTISTEP=False, cfgpp=0.0, implicit_steps=0, reverse_weight=0.0, exp_mode=False,
latent_guide=None, latent_guide_inv=None, latent_guide_weight=0.0, latent_guide_weights=None, guide_mode="blend",
GARBAGE_COLLECT=False, mask=None, LGW_MASK_RESCALE_MIN=True, sigmas_override=None, t_is=None,
):
extra_args = {} if extra_args is None else extra_args
if sigmas_override is not None:
sigmas = sigmas_override.clone()
sigmas = sigmas.clone() * d_noise
sigmin = model.inner_model.inner_model.model_sampling.sigma_min
sigmax = model.inner_model.inner_model.model_sampling.sigma_max
UNSAMPLE = False
if sigmas[0] == 0.0: #remove padding used to avoid need for model patch with noise inversion
UNSAMPLE = True
sigmas = sigmas[1:-1]
if mask is None:
mask = torch.ones_like(x)
LGW_MASK_RESCALE_MIN = False
else:
mask = mask.unsqueeze(1)
mask = mask.repeat(1, x.shape[1], 1, 1)
mask = F.interpolate(mask, size=(x.shape[2], x.shape[3]), mode='bilinear', align_corners=False)
mask = mask.to(x.dtype).to(x.device)
y0, y0_inv = torch.zeros_like(x), torch.zeros_like(x)
if latent_guide is not None:
if sigmas[0] > sigmas[1]:
y0 = latent_guide = model.inner_model.inner_model.process_latent_in(latent_guide['samples']).clone().to(x.device)
else:
x = model.inner_model.inner_model.process_latent_in(latent_guide['samples']).clone().to(x.device)
if latent_guide_inv is not None:
if sigmas[0] > sigmas[1]:
y0_inv = latent_guide_inv = model.inner_model.inner_model.process_latent_in(latent_guide_inv['samples']).clone().to(x.device)
elif UNSAMPLE and mask is not None:
x = mask * x + (1-mask) * model.inner_model.inner_model.process_latent_in(latent_guide_inv['samples']).clone().to(x.device)
uncond = [torch.full_like(x, 0.0)]
if cfgpp != 0.0:
def post_cfg_function(args):
uncond[0] = args["uncond_denoised"]
return args["denoised"]
model_options = extra_args.get("model_options", {}).copy()
extra_args["model_options"] = comfy.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)
if noise_seed == -1:
seed = torch.initial_seed() + 1
else:
seed = noise_seed
if noise_sampler_type == "fractal":
noise_sampler = NOISE_GENERATOR_CLASSES.get(noise_sampler_type)(x=x, seed=seed, sigma_min=sigmin, sigma_max=sigmax)
noise_sampler.alpha = alpha
noise_sampler.k = k
noise_sampler.scale = scale
else:
noise_sampler = NOISE_GENERATOR_CLASSES_SIMPLE.get(noise_sampler_type)(x=x, seed=seed, sigma_min=sigmin, sigma_max=sigmax)
if UNSAMPLE and sigmas[0] < sigmas[1]: #sigma_next > sigma:
y0 = noise_sampler(sigma=sigmax, sigma_next=sigmin)
y0 = (y0 - y0.mean()) / y0.std()
y0_inv = noise_sampler(sigma=sigmax, sigma_next=sigmin)
y0_inv = (y0_inv - y0_inv.mean()) / y0_inv.std()
order, model_call, alpha_fn, t_fn, sigma_fn, h_fn, FSAL, EPS_PRED = get_rk_methods_order_and_fn(rk_type)
if exp_mode:
model_call = get_denoised
alpha_fn = lambda neg_h: torch.exp(neg_h)
t_fn = lambda sigma: sigma.log().neg()
sigma_fn = lambda t: t.neg().exp()
xi, ki, ki_u = [torch.zeros_like(x)]*(order+2), [torch.zeros_like(x)]*(order+1), [torch.zeros_like(x)]*(order+1)
h, h_prev, h_prev2 = None, None, None
xi[0] = x
for _ in trange(len(sigmas)-1, disable=disable):
sigma, sigma_next = sigmas[_], sigmas[_+1]
if sigma_next == 0.0:
rk_type = "euler"
eta, eta_var = 0, 0
order, model_call, alpha_fn, t_fn, sigma_fn, h_fn, FSAL, EPS_PRED = get_rk_methods_order_and_fn(rk_type)
sigma_up, sigma, sigma_down, alpha_ratio = get_res4lyf_step_with_model(model, sigma, sigma_next, eta, eta_var, noise_mode, h_fn(sigma_next,sigma) )
t_down, t = t_fn(sigma_down), t_fn(sigma)
h = h_fn(sigma_down, sigma)
c2, c3 = get_res4lyf_half_step3(sigma, sigma_down, c2, c3, t_fn=t_fn, sigma_fn=sigma_fn, t_fn_formula=t_fn_formula, sigma_fn_formula=sigma_fn_formula)
ab, ci, multistep_stages, EPS_PRED = get_rk_methods_coeff(rk_type, h, c1, c2, c3, h_prev, h_prev2, _, sigmas)
order = len(ci)-1
if exp_mode:
for i in range(order):
for j in range(order):
ab[i][j] = ab[i][j] * phi(1, -h * ci[i+1])
if isinstance(model.inner_model.inner_model.model_sampling, comfy.model_sampling.CONST) == False and noise_mode == "hard" and sigma_next > 0.0:
noise = noise_sampler(sigma=sigmas[_], sigma_next=sigmas[_+1])
noise = torch.nan_to_num((noise - noise.mean()) / noise.std(), 0.0)
xi[0] = alpha_ratio * xi[0] + noise * s_noise * sigma_up
xi_0 = xi[0] # needed for implicit sampling
if (MULTISTEP == False and FSAL == False) or _ == 0:
ki[0] = model_call(model, xi_0, sigma, **extra_args)
if EPS_PRED and rk_type.startswith("deis"):
ki[0] = (xi_0 - ki[0]) / sigma
ki[0] = ki[0] * (sigma_down-sigma)/(sigma_next-sigma)
ki_u[0] = uncond[0]
if cfgpp != 0.0:
ki[0] = uncond[0] + cfgpp * (ki[0] - uncond[0])
ki_u[0] = uncond[0]
for iteration in range(implicit_steps+1):
for i in range(multistep_stages, order):
if implicit_steps > 0 and iteration > 0 and implicit_sampler_name != "default":
ab, ci, multistep_stages, EPS_PRED = get_rk_methods_coeff(implicit_sampler_name, h, c1, c2, c3, h_prev, h_prev2, _, sigmas)
order = len(ci)-1
if len(ki) < order + 1:
last_value_ki = ki[-1]
last_value_ki_u = ki_u[-1]
ki.extend( [last_value_ki] * ((order + 1) - len(ki)))
ki_u.extend([last_value_ki_u] * ((order + 1) - len(ki_u)))
if len(xi) < order + 2:
xi.extend([torch.zeros_like(xi[0])] * ((order + 2) - len(xi)))
ki[0] = model_call(model, xi_0, sigma, **extra_args)
ki_u[0] = uncond[0]
sigma_mid = sigma_fn(t + h*ci[i+1])
alpha_t_1 = alpha_t_1_inv = torch.exp(torch.log(sigma_down/sigma) * ci[i+1] )
if sigma_next > sigma:
alpha_t_1_inv = torch.nan_to_num( torch.exp(torch.log((sigmax - sigma_down)/(sigmax - sigma)) * ci[i+1]), 1.)
if LGW_MASK_RESCALE_MIN:
lgw_mask = mask * (1 - latent_guide_weights[_]) + latent_guide_weights[_]
lgw_mask_inv = (1-mask) * (1 - latent_guide_weights[_]) + latent_guide_weights[_]
else:
lgw_mask = mask * latent_guide_weights[_]
lgw_mask_inv = (1-mask) * latent_guide_weights[_]
ks, ks_u, ys, ys_inv = torch.zeros_like(x), torch.zeros_like(x), torch.zeros_like(x), torch.zeros_like(x)
for j in range(order):
ks += ab[i][j] * ki[j]
ks_u += ab[i][j] * ki_u[j]
ys += ab[i][j] * y0
ys_inv += ab[i][j] * y0_inv
if EPS_PRED and rk_type.startswith("deis"):
epsilon = (h * ks) / (sigma_down - sigma) #xi[(i+1)%order] = xi_0 + h*ks
ks = xi_0 - epsilon * sigma # denoised
else:
if implicit_sampler_name.startswith("lobatto") == False:
ks /= sum(ab[i])
elif iteration == 0:
ks /= sum(ab[i])
if UNSAMPLE == False and latent_guide is not None and latent_guide_weights[_] > 0.0:
if guide_mode == "hard_light":
lg = latent_guide * sum(ab[i])
if EPS_PRED:
lg = (alpha_fn(-h*ci[i+1]) * xi[0] - latent_guide) / (sigma_fn(t + h*ci[i]) + 1e-8)
hard_light_blend_1 = hard_light_blend(lg, ks)
ks = (1 - lgw_mask) * ks + lgw_mask * hard_light_blend_1
elif guide_mode == "mean_std":
ks2 = torch.zeros_like(x)
for n in range(latent_guide.shape[1]):
ks2[0][n] = (ks[0][n] - ks[0][n].mean()) / ks[0][n].std()
ks2[0][n] = (ks2[0][n] * latent_guide[0][n].std()) + latent_guide[0][n].mean()
ks = (1 - lgw_mask) * ks + lgw_mask * ks2
elif guide_mode == "mean":
ks2 = torch.zeros_like(x)
for n in range(latent_guide.shape[1]):
ks2[0][n] = (ks[0][n] - ks[0][n].mean())
ks2[0][n] = (ks2[0][n]) + latent_guide[0][n].mean()
ks3 = torch.zeros_like(x)
for n in range(latent_guide.shape[1]):
ks3[0][n] = (ks[0][n] - ks[0][n].mean())
ks3[0][n] = (ks3[0][n]) + latent_guide_inv[0][n].mean()
ks = (1 - lgw_mask) * ks + lgw_mask * ks2
ks = (1 - lgw_mask_inv) * ks + lgw_mask_inv * ks3
elif guide_mode == "std":
ks2 = torch.zeros_like(x)
for n in range(latent_guide.shape[1]):
ks2[0][n] = (ks[0][n]) / ks[0][n].std()
ks2[0][n] = (ks2[0][n] * latent_guide[0][n].std())
ks = (1 - lgw_mask) * ks + lgw_mask * ks2
elif guide_mode == "blend":
ks = (1 - lgw_mask) * ks + lgw_mask * ys #+ (1-lgw_mask) * latent_guide_inv
ks = (1 - lgw_mask_inv) * ks + lgw_mask_inv * ys_inv
elif guide_mode == "inversion":
UNSAMPLE = True
cfgpp_term = cfgpp*h*(ks - ks_u)
xi[(i+1)%order] = (1-UNSAMPLE * lgw_mask) * (alpha_t_1 * (xi_0 + cfgpp_term) + (1 - alpha_t_1) * ks ) \
+ UNSAMPLE * lgw_mask * (alpha_t_1_inv * (xi_0 + cfgpp_term) + (1 - alpha_t_1_inv) * ys )
if UNSAMPLE:
xi[(i+1)%order] = (1-lgw_mask_inv) * xi[(i+1)%order] + UNSAMPLE * lgw_mask_inv * (alpha_t_1_inv * (xi_0 + cfgpp_term) + (1 - alpha_t_1_inv) * ys_inv )
if (i+1)%order > 0 and (i+1)%order > multistep_stages-1:
if GARBAGE_COLLECT: gc.collect(); torch.cuda.empty_cache()
ki[i+1] = model_call(model, xi[i+1], sigma_fn(t + h*ci[i+1]), **extra_args)
if EPS_PRED and rk_type.startswith("deis"):
ki[i+1] = (xi[i+1] - ki[i+1]) / sigma_fn(t + h*ci[i+1])
ki[i+1] = ki[i+1] * (sigma_down-sigma)/(sigma_next-sigma)
ki_u[i+1] = uncond[0]
if FSAL and _ > 0:
ki [0] = ki[order-1]
ki_u[0] = ki_u[order-1]
if MULTISTEP and _ > 0:
ki [0] = denoised
ki_u[0] = ki_u[order-1]
for ms in range(multistep_stages):
ki [multistep_stages - ms] = ki [multistep_stages - ms - 1]
ki_u[multistep_stages - ms] = ki_u[multistep_stages - ms - 1]
if iteration < implicit_steps and implicit_sampler_name == "default":
ki [0] = model_call(model, xi[0], sigma_down, **extra_args)
ki_u[0] = uncond[0]
elif iteration == implicit_steps and implicit_sampler_name != "default" and implicit_steps > 0:
ks, ks_u, ys, ys_inv = torch.zeros_like(x), torch.zeros_like(x), torch.zeros_like(x), torch.zeros_like(x)
for j in range(order):
ks += ab[i+1][j] * ki[j]
ks_u += ab[i+1][j] * ki_u[j]
ys += ab[i+1][j] * y0
ys_inv += ab[i+1][j] * y0_inv
ks /= sum(ab[i+1])
cfgpp_term = cfgpp*h*(ks - ks_u) #GUIDES NOT FULLY IMPLEMENTED HERE WITH IMPLICIT FINAL STEP
xi[(i+1)%order] = (1-UNSAMPLE * lgw_mask) * (alpha_t_1 * (xi_0 + cfgpp_term) + (1 - alpha_t_1) * ks ) \
+ UNSAMPLE * lgw_mask * (alpha_t_1_inv * (xi_0 + cfgpp_term) + (1 - alpha_t_1_inv) * ys )
if UNSAMPLE:
xi[(i+1)%order] = (1-lgw_mask_inv) * xi[(i+1)%order] + UNSAMPLE * lgw_mask_inv * (alpha_t_1_inv * (xi_0 + cfgpp_term) + (1 - alpha_t_1_inv) * ys_inv )
if EPS_PRED == True and exp_mode == False and not rk_type.startswith("deis"):
denoised = alpha_fn(-h*ci[i+1]) * xi[0] - sigma * ks
elif EPS_PRED == True and rk_type.startswith("deis"):
epsilon = (h * ks) / (sigma_down - sigma)
denoised = xi_0 - epsilon * sigma # denoised
elif iteration == implicit_steps and implicit_sampler_name != "default" and implicit_steps > 0:
denoised = ks
else:
denoised = ks / sum(ab[i])
"""if iteration < implicit_steps and implicit_sampler_name != "default":
for idx in range(len(ki)):
ki[idx] = denoised"""
if callback is not None:
callback({'x': xi[0], 'i': _, 'sigma': sigma, 'sigma_next': sigma_next, 'denoised': denoised})
if (isinstance(model.inner_model.inner_model.model_sampling, comfy.model_sampling.CONST) or noise_mode != "hard") and sigma_next > 0.0:
noise = noise_sampler(sigma=sigma, sigma_next=sigma_next)
noise = (noise - noise.mean()) / noise.std()
if guide_mode == "noise_mean":
noise2 = torch.zeros_like(x)
for n in range(latent_guide.shape[1]):
noise2[0][n] = (noise[0][n] - noise[0][n].mean())
noise2[0][n] = (noise2[0][n]) + latent_guide[0][n].mean()
noise = (1 - lgw_mask) * noise + lgw_mask * noise2
xi[0] = alpha_ratio * xi[0] + noise * s_noise * sigma_up
h_prev2 = h_prev
h_prev = h
return xi[0]
def get_irk_explicit_sigmas(model, x, sigmas, eta, eta_var, noise_mode, c1, c2, c3, rk, irk, rk_type, implicit_sampler_name, t_fn_formula="", sigma_fn_formula=""):
s_in = x.new_ones([x.shape[0]])
irk_sigmas = torch.empty_like(sigmas)
eta, eta_var = 0, 0
for _ in range(len(sigmas)-1):
sigma, sigma_next = sigmas[_], sigmas[_+1]
sigma_up, sigma, sigma_down, alpha_ratio = get_res4lyf_step_with_model(model, sigma, sigma_next, eta, eta_var, noise_mode, rk.h_fn(sigma_next,sigma) )
h = rk.h_fn(sigma_down, sigma)
h_irk = irk.h_fn(sigma_down, sigma)
c2, c3 = get_res4lyf_half_step3(sigma, sigma_down, c2, c3, t_fn=rk.t_fn, sigma_fn=rk.sigma_fn, t_fn_formula=t_fn_formula, sigma_fn_formula=sigma_fn_formula)
rk. set_coeff(rk_type, h, c1, c2, c3, _, sigmas, sigma, sigma_down)
irk.set_coeff(implicit_sampler_name, h_irk, c1, c2, c3, _, sigmas, sigma, sigma_down)
s_irk = [( irk.sigma_fn(irk.t_fn(sigma) + h*c_)) * s_in for c_ in irk.c]
s_irk.append(sigma)
s_all = sorted(set(s_irk), reverse=True)
s_irk = s_irk[:-1]
s_all[0] = s_all[0].unsqueeze(dim=0)
s_all_sigmas = torch.stack(s_all, dim=0).squeeze(dim=1)
irk_sigmas = torch.cat((irk_sigmas, s_all_sigmas), dim=0)
return irk_sigmas
from .rk_method import RK_Method, RK_Method_Linear, RK_Method_Exponential
@torch.no_grad()
def sample_rk_beta(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None, noise_sampler_type="brownian", noise_mode="hard", noise_seed=-1, rk_type="res_2m", implicit_sampler_name="default",
sigma_fn_formula="", t_fn_formula="",
eta=0.0, eta_var=0.0, s_noise=1., d_noise=1., alpha=-1.0, k=1.0, scale=0.1, c1=0.0, c2=0.5, c3=1.0, MULTISTEP=False, cfgpp=0.0, implicit_steps=0, reverse_weight=0.0, exp_mode=False,
latent_guide=None, latent_guide_inv=None, latent_guide_weights=None, guide_mode="blend", unsampler_type="linear",
GARBAGE_COLLECT=False, mask=None, LGW_MASK_RESCALE_MIN=True, sigmas_override=None, t_is=None,sde_noise=None,
):
extra_args = {} if extra_args is None else extra_args
s_in = x.new_ones([x.shape[0]])
if len(sde_noise) > 0 and sigmas[1] > sigmas[2]:
SDE_NOISE_EXTERNAL = True