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"""
https://arxiv.org/abs/2312.07537
"""
import math
import torch
import torch.fft as fft
import torch.nn.functional as F
def freq_mix_3d(x, noise, LPF):
"""
Noise reinitialization.
Args:
x: diffused latent
noise: randomly sampled noise
LPF: low pass filter
"""
# FFT
x_freq = fft.fftn(x, dim=(-3, -2, -1))
x_freq = fft.fftshift(x_freq, dim=(-3, -2, -1))
noise_freq = fft.fftn(noise, dim=(-3, -2, -1))
noise_freq = fft.fftshift(noise_freq, dim=(-3, -2, -1))
# frequency mix
HPF = 1 - LPF
x_freq_low = x_freq * LPF
noise_freq_high = noise_freq * HPF
x_freq_mixed = x_freq_low + noise_freq_high # mix in freq domain
# IFFT
x_freq_mixed = fft.ifftshift(x_freq_mixed, dim=(-3, -2, -1))
x_mixed = fft.ifftn(x_freq_mixed, dim=(-3, -2, -1)).real
return x_mixed
def get_freq_filter(shape, device, filter_type, n, d_s, d_t):
"""
Form the frequency filter for noise reinitialization.
Args:
shape: shape of latent (B, C, T, H, W)
filter_type: type of the freq filter
n: (only for butterworth) order of the filter, larger n ~ ideal, smaller n ~ gaussian
d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
d_t: normalized stop frequency for temporal dimension (0.0-1.0)
"""
if filter_type == "gaussian":
return gaussian_low_pass_filter(shape=shape, d_s=d_s, d_t=d_t).to(device)
elif filter_type == "ideal":
return ideal_low_pass_filter(shape=shape, d_s=d_s, d_t=d_t).to(device)
elif filter_type == "box":
return box_low_pass_filter(shape=shape, d_s=d_s, d_t=d_t).to(device)
elif filter_type == "butterworth":
return butterworth_low_pass_filter(shape=shape, n=n, d_s=d_s, d_t=d_t).to(device)
else:
raise NotImplementedError
def gaussian_low_pass_filter(shape, d_s=0.25, d_t=0.25):
"""
Compute the gaussian low pass filter mask.
Args:
shape: shape of the filter (volume)
d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
d_t: normalized stop frequency for temporal dimension (0.0-1.0)
"""
T, H, W = shape[-3], shape[-2], shape[-1]
mask = torch.zeros(shape)
if d_s==0 or d_t==0:
return mask
for t in range(T):
for h in range(H):
for w in range(W):
d_square = (((d_s/d_t)*(2*t/T-1))**2 + (2*h/H-1)**2 + (2*w/W-1)**2)
mask[..., t,h,w] = math.exp(-1/(2*d_s**2) * d_square)
return mask
def butterworth_low_pass_filter(shape, n=4, d_s=0.25, d_t=0.25):
"""
Compute the butterworth low pass filter mask.
Args:
shape: shape of the filter (volume)
n: order of the filter, larger n ~ ideal, smaller n ~ gaussian
d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
d_t: normalized stop frequency for temporal dimension (0.0-1.0)
"""
T, H, W = shape[-3], shape[-2], shape[-1]
mask = torch.zeros(shape)
if d_s==0 or d_t==0:
return mask
for t in range(T):
for h in range(H):
for w in range(W):
d_square = (((d_s/d_t)*(2*t/T-1))**2 + (2*h/H-1)**2 + (2*w/W-1)**2)
mask[..., t,h,w] = 1 / (1 + (d_square / d_s**2)**n)
return mask
def ideal_low_pass_filter(shape, d_s=0.25, d_t=0.25):
"""
Compute the ideal low pass filter mask.
Args:
shape: shape of the filter (volume)
d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
d_t: normalized stop frequency for temporal dimension (0.0-1.0)
"""
T, H, W = shape[-3], shape[-2], shape[-1]
mask = torch.zeros(shape)
if d_s==0 or d_t==0:
return mask
for t in range(T):
for h in range(H):
for w in range(W):
d_square = (((d_s/d_t)*(2*t/T-1))**2 + (2*h/H-1)**2 + (2*w/W-1)**2)
mask[..., t,h,w] = 1 if d_square <= d_s*2 else 0
return mask
def box_low_pass_filter(shape, d_s=0.25, d_t=0.25):
"""
Compute the ideal low pass filter mask (approximated version).
Args:
shape: shape of the filter (volume)
d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
d_t: normalized stop frequency for temporal dimension (0.0-1.0)
"""
T, H, W = shape[-3], shape[-2], shape[-1]
mask = torch.zeros(shape)
if d_s==0 or d_t==0:
return mask
threshold_s = round(int(H // 2) * d_s)
threshold_t = round(T // 2 * d_t)
cframe, crow, ccol = T // 2, H // 2, W //2
mask[..., cframe - threshold_t:cframe + threshold_t, crow - threshold_s:crow + threshold_s, ccol - threshold_s:ccol + threshold_s] = 1.0
return mask
@torch.no_grad()
def init_filter(video_length, height, width, filter_params_method="gaussian", filter_params_n=4, filter_params_d_s=0.25, filter_params_d_t=0.25, num_channels_latents=4, device='cpu'):
# initialize frequency filter for noise reinitialization
batch_size = 1
num_channels_latents = num_channels_latents
filter_shape = [
batch_size,
num_channels_latents,
video_length,
height,
width,
]
freq_filter = get_freq_filter(
filter_shape,
device=device,
filter_type=filter_params_method,
n=filter_params_n if filter_params_method=="butterworth" else None,
d_s=filter_params_d_s,
d_t=filter_params_d_t
)
return freq_filter
def FFTInit(noisy_latent, noise):
dtype = noisy_latent.dtype
freq_filter = init_filter(
video_length=noisy_latent.shape[2],
height=noisy_latent.shape[3],
width=noisy_latent.shape[4],
device=noisy_latent.device
)
# make it float32 to accept any kinds of resolution
latents = freq_mix_3d(noisy_latent.to(dtype=torch.float32), noise.to(dtype=torch.float32), LPF=freq_filter)
latents = latents.to(dtype)
return latents |