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simplest_PyramidFlow.py
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simplest_PyramidFlow.py
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"""
A simple python script can quickly learn how to use `autoFlow` framework.
"""
import torch # torch >= 1.9.0
import torch.nn as nn
import torch.nn.functional as F
from autoFlow import InvertibleModule
from autoFlow import SequentialNF
""" Estimate affine layer parameters ,`exp(s)` and `t()` """
class AffineParamBlock(nn.Module):
def __init__(self, in_ch):
super(AffineParamBlock, self).__init__()
self.clamp = 3
self.conv = nn.Sequential(
nn.Conv2d(in_ch, 2*in_ch, kernel_size=7, padding=7//2, bias=False),
nn.LeakyReLU(),
nn.Conv2d(2*in_ch, 2*in_ch, kernel_size=7, padding=7//2, bias=False),
)
def forward(self, input):
output = self.conv(input)
_dlogdet, bias = output.chunk(2, 1)
dlogdet = self.clamp * 0.636 * torch.atan(_dlogdet / self.clamp) # Soft clipping
scale = torch.exp(dlogdet)
return (scale, bias), dlogdet # scale * x + bias
""" Single affine coupling layer, there are two kinds of fusion: `up` or `down` """
class FlowBlock(InvertibleModule):
def __init__(self, channel, direct):
super(FlowBlock, self).__init__()
assert direct in ['up', 'down']
self.direct = direct
self.affineParams = AffineParamBlock(channel)
def forward(self, inputs, logdets):
x0, x1 = inputs
logdet0, logdet1 = logdets
if self.direct == 'up':
y10 = F.interpolate(x1, size=x0.shape[2:], mode='nearest') # interpolation first in up-sampling
(scale0, bias0), dlogdet0 = self.affineParams(y10)
z0, z1 = scale0*x0+bias0, x1
dlogdet1 = 0
else:
(scale10, bias10), dlogdet10 = self.affineParams(x0)
scale1, bias1, dlogdet1 = F.interpolate(scale10, size=x1.shape[2:], mode='nearest'),\
F.interpolate(bias10, size=x1.shape[2:], mode='nearest'),\
F.interpolate(dlogdet10, size=x1.shape[2:], mode='nearest') # interpolation after in down-sampling
z0, z1 = x0, scale1*x1+bias1
dlogdet0 = 0
outputs = (z0, z1)
out_logdets = (logdet0+dlogdet0, logdet1+dlogdet1)
return outputs, out_logdets
def inverse(self, outputs, logdets):
z0, z1 = outputs
logdet0, logdet1 = logdets
if self.direct == 'up':
z10 = F.interpolate(z1, size=z0.shape[2:], mode='nearest') # interpolation first in up-sampling
(scale0, bias0), dlogdet0 = self.affineParams(z10)
x0, x1 = (z0-bias0)/scale0, z1
dlogdet1 = 0
else:
(scale01, bias01), dlogdet01 = self.affineParams(z0)
scale1, bias1, dlogdet1 = F.interpolate(scale01, size=z1.shape[2:], mode='nearest'),\
F.interpolate(bias01, size=z1.shape[2:], mode='nearest'),\
F.interpolate(dlogdet01, size=z1.shape[2:], mode='nearest') # interpolation after in down-sampling
x0, x1 = z0, (z1-bias1)/scale1
dlogdet0 = 0
inputs = (x0, x1)
in_logdets = (logdet0-dlogdet0, logdet1-dlogdet1)
return inputs, in_logdets
""" semi-invertible 1x1Conv """
class Invertible_1x1Conv(nn.Conv2d):
def __init__(self, in_channels, out_channels ) -> None:
assert out_channels >= in_channels
super().__init__(in_channels, out_channels, kernel_size=1, bias=False)
def inverse(self, output):
b, c, h, w = output.shape
A = self.weight[..., 0, 0] # outch, inch
B = output.permute([1,0,2,3]).reshape(c, -1) # outch, bhw
X = torch.linalg.lstsq(A, B) # AX=B
return X.solution.reshape(-1, b, h, w).permute([1, 0, 2, 3])
@property
def logdet(self):
w = self.weight.squeeze() # out,in
return 0.5*torch.logdet(w.T@w)
""" `filter2d` function from kornia """
def kornia_filter2d(
input: torch.Tensor, kernel: torch.Tensor,
) -> torch.Tensor:
# prepare kernel
b, c, h, w = input.shape
tmp_kernel: torch.Tensor = kernel.unsqueeze(1).to(input)
tmp_kernel = tmp_kernel.expand(-1, c, -1, -1)
height, width = tmp_kernel.shape[-2:]
# kernel and input tensor reshape to align element-wise or batch-wise params
tmp_kernel = tmp_kernel.reshape(-1, 1, height, width)
input = input.view(-1, tmp_kernel.size(0), input.size(-2), input.size(-1))
# convolve the tensor with the kernel.
output = F.conv2d(input, tmp_kernel, groups=tmp_kernel.size(0), padding=0, stride=1)
return output
""" Invertible Pyramid (aka LaplacianPyramid) """
class LaplacianPyramid(nn.Module):
def __init__(self, num_levels) -> None:
super().__init__()
self.kernel = torch.tensor(
[
[
[1.0, 4.0, 6.0, 4.0, 1.0],
[4.0, 16.0, 24.0, 16.0, 4.0],
[6.0, 24.0, 36.0, 24.0, 6.0],
[4.0, 16.0, 24.0, 16.0, 4.0],
[1.0, 4.0, 6.0, 4.0, 1.0],
]
]
)/ 256.0
self.num_levels = num_levels - 1 # total num_levels layers
# which the last layer is the last Gaussian pyramid layer.
def _pyramid_down(self, input, pad_mode='reflect'):
if not len(input.shape) == 4:
raise ValueError(f'Invalid img shape, we expect BCHW, got: {input.shape}')
# blur
img_pad = F.pad(input, (2,2,2,2), mode=pad_mode)
img_blur = kornia_filter2d(img_pad, kernel=self.kernel)
# downsample
out = F.interpolate(img_blur, scale_factor=0.5, mode='nearest')
return out
def _pyramid_up(self, input, size, pad_mode='reflect'):
if not len(input.shape) == 4:
raise ValueError(f'Invalid img shape, we expect BCHW, got: {input.shape}')
# upsample
img_up = F.interpolate(input, size=size, mode='nearest', )
# blur
img_pad = F.pad(img_up, (2,2,2,2), mode=pad_mode)
img_blur = kornia_filter2d(img_pad, kernel=self.kernel)
return img_blur
def build_pyramid(self, input):
gp, lp = [input], []
for _ in range(self.num_levels):
gp.append(self._pyramid_down(gp[-1]))
for layer in range(self.num_levels):
curr_gp = gp[layer]
next_gp = self._pyramid_up(gp[layer+1], size=curr_gp.shape[2:])
lp.append(curr_gp - next_gp)
lp.append(gp[self.num_levels])
return lp
def compose_pyramid(self, lp):
rs = lp[-1]
for i in range(self.num_levels-1, -1, -1):
rs = self._pyramid_up(rs, size=lp[i].shape[2:])
rs = torch.add(rs, lp[i])
return rs
""" The simplest PyramidFlow (w/o Volume Normalization or other tricks) to test `autoFlow` framework. """
class SimpleTestFlow(SequentialNF):
def __init__(self, modules, channel):
super().__init__(modules)
self.inconv = Invertible_1x1Conv(3, channel)
self.pyramid = LaplacianPyramid(2)
def forward(self, img):
feat = self.inconv(img)
pyramid = self.pyramid.build_pyramid(feat)
logdets = tuple(torch.zeros_like(pyramid_j) for pyramid_j in pyramid)
return super().forward(pyramid, logdets)
def inverse(self, pyramid_out, logdets_out):
pyramid_in, logdets_in = super().inverse(pyramid_out, logdets_out)
feat = self.pyramid.compose_pyramid(pyramid_in)
rev_img = self.inconv.inverse(feat)
return rev_img, logdets_in
if __name__ == '__main__':
torch.random.manual_seed(0)
num_stack = 3
channel = 64
# Module sequence
modules = []
for _ in range(num_stack):
modules.append(FlowBlock(channel, direct='up'))
modules.append(FlowBlock(channel, direct='down'))
# NF
flowNF = SimpleTestFlow(modules, channel=channel).cuda()
img = torch.randn(2, 3, 256, 256).cuda()
pyramid_out, logdets_out = flowNF.forward(img)
rev_img, _ = flowNF.inverse(pyramid_out, logdets_out)
# Print results
dimg = torch.abs(img - rev_img)
print(f'Maximum Error: {dimg.max().item():.3e}') # 2.146e-06