利用扩散模型DDPM生成高分辨率图像（生成高保真图像项目实践）
Mindspore框架利用扩散模型DDPM生成高分辨率图像|（一）关于denoising diffusion probabilistic model （DDPM）模型
Mindspore框架利用扩散模型DDPM生成高分辨率图像|（二）数据集准备与处理
Mindspore框架利用扩散模型DDPM生成高分辨率图像|（三）模型训练与推理实践
一、 关于denoising diffusion probabilistic model （DDPM）模型
注意：本文的Diffusion扩散模型是基于denoising diffusion probabilistic model （DDPM模型）
利用diffusion模型，生成高保真图像，就是将低分辨率图像，转成高保真图像的方法。pytorch实现算法代码：算法原理，就是将噪声从一些简单分布转换为数据样本，Diffusion也是从纯噪声开始通过一个神经网络学习逐步去噪，最终得到一个实际图像。
本文介绍，用mindspore实现DDPM模型。
1.1 模型简介
Diffusion对于图像的处理包括以下两个过程：
1）选择的固定（或预定义）正向扩散过程 ：它逐渐将高斯噪声添加到图像中，直到最终得到纯噪声；
2）一个学习的反向去噪的扩散过程 ：通过训练神经网络从纯噪声开始逐渐对图像去噪，直到最终得到一个实际的图像。
由t索引的正向和反向过程都发生在某些有限时间步长 （DDPM作者使用 ）内。从开始，在数据分布中采样真实图像
（本文使用一张来自ImageNet的猫图像形象的展示了diffusion正向添加噪声的过程），正向过程在每个时间步长 都从高斯分布中采样一些噪声，再添加到上一个时刻的图像中。假定给定一个足够大的 和一个在每个时间步长添加噪声的良好时间表，您最终会在 通过渐进的过程得到所谓的各向同性的高斯分布。
1.2 Diffusion 前向过程
1.3 Diffusion 逆向过程
二、 DDPM模型实现
（1）将图像变成纯噪声
输入图片，输出仍然是图片。此处，用U-Net来预测噪声图片。
作用：每个图像和生成的纯噪声构成逆行过程的数据集。
（2）构建逆向过程的模型，实现噪声输入，图像输出。模型依旧是U-Net结构。
作用：模型可以对输入有效保真。
Tips:安装依赖MindSpore、download、dataset、matplotlib以及tqdm
import math
from functools import partial
import matplotlib.pyplot as plt
from tqdm.auto import tqdm
import numpy as np
from multiprocessing import cpu_count
from download import download
import mindspore as ms
import mindspore.nn as nn
import mindspore.ops as ops
from mindspore import Tensor, Parameter
from mindspore import dtype as mstype
from mindspore.dataset.vision import Resize, Inter, CenterCrop, ToTensor, RandomHorizontalFlip, ToPIL
from mindspore.common.initializer import initializer
from mindspore.amp import DynamicLossScaler
ms.set_seed(0)
构建Diffusion模型
2.1 定义了一些辅助函数和类
def rearrange(head, inputs):
b, hc, x, y = inputs.shape
c = hc // head
return inputs.reshape((b, head, c, x * y))
def rsqrt(x):
res = ops.sqrt(x)
return ops.inv(res)
def randn_like(x, dtype=None):
if dtype is None:
dtype = x.dtype
res = ops.standard_normal(x.shape).astype(dtype)
return res
def randn(shape, dtype=None):
if dtype is None:
dtype = ms.float32
res = ops.standard_normal(shape).astype(dtype)
return res
def randint(low, high, size, dtype=ms.int32):
res = ops.uniform(size, Tensor(low, dtype), Tensor(high, dtype), dtype=dtype)
return res
def exists(x):
return x is not None
def default(val, d):
if exists(val):
return val
return d() if callable(d) else d
def _check_dtype(d1, d2):
if ms.float32 in (d1, d2):
return ms.float32
if d1 == d2:
return d1
raise ValueError('dtype is not supported.')
# 上采样
def Upsample(dim):
return nn.Conv2dTranspose(dim, dim, 4, 2, pad_mode="pad", padding=1)
# 下采样
def Downsample(dim):
return nn.Conv2d(dim, dim, 4, 2, pad_mode="pad", padding=1)
class Residual(nn.Cell):
def __init__(self, fn):
super().__init__()
self.fn = fn
def construct(self, x, *args, **kwargs):
return self.fn(x, *args, **kwargs) + x
2.2 定义位置向量：SinusoidalPositionEmbeddings
class SinusoidalPositionEmbeddings(nn.Cell):
def __init__(self, dim):
super().__init__()
self.dim = dim
half_dim = self.dim // 2
emb = math.log(10000) / (half_dim - 1)
emb = np.exp(np.arange(half_dim) * - emb)
self.emb = Tensor(emb, ms.float32)
def construct(self, x):
emb = x[:, None] * self.emb[None, :]
emb = ops.concat((ops.sin(emb), ops.cos(emb)), axis=-1)
return emb
2.3 定义U-Net模型
U-Net架构中，选择了ConvNeXT块构建U-Net模型。
class Block(nn.Cell):
def __init__(self, dim, dim_out, groups=1):
super().__init__()
self.proj = nn.Conv2d(dim, dim_out, 3, pad_mode="pad", padding=1)
self.proj = c(dim, dim_out, 3, padding=1, pad_mode='pad')
self.norm = nn.GroupNorm(groups, dim_out)
self.act = nn.SiLU()
def construct(self, x, scale_shift=None):
x = self.proj(x)
x = self.norm(x)
if exists(scale_shift):
scale, shift = scale_shift
x = x * (scale + 1) + shift
x = self.act(x)
return x
class ConvNextBlock(nn.Cell):
def __init__(self, dim, dim_out, *, time_emb_dim=None, mult=2, norm=True):
super().__init__()
self.mlp = (
nn.SequentialCell(nn.GELU(), nn.Dense(time_emb_dim, dim))
if exists(time_emb_dim)
else None
)
self.ds_conv = nn.Conv2d(dim, dim, 7, padding=3, group=dim, pad_mode="pad")
self.net = nn.SequentialCell(
nn.GroupNorm(1, dim) if norm else nn.Identity(),
nn.Conv2d(dim, dim_out * mult, 3, padding=1, pad_mode="pad"),
nn.GELU(),
nn.GroupNorm(1, dim_out * mult),
nn.Conv2d(dim_out * mult, dim_out, 3, padding=1, pad_mode="pad"),
)
self.res_conv = nn.Conv2d(dim, dim_out, 1) if dim != dim_out else nn.Identity()
def construct(self, x, time_emb=None):
h = self.ds_conv(x)
if exists(self.mlp) and exists(time_emb):
assert exists(time_emb), "time embedding must be passed in"
condition = self.mlp(time_emb)
condition = condition.expand_dims(-1).expand_dims(-1)
h = h + condition
h = self.net(h)
return h + self.res_conv(x)
2.4 Attention模块
class Attention(nn.Cell):
def __init__(self, dim, heads=4, dim_head=32):
super().__init__()
self.scale = dim_head ** -0.5
self.heads = heads
hidden_dim = dim_head * heads
self.to_qkv = nn.Conv2d(dim, hidden_dim * 3, 1, pad_mode='valid', has_bias=False)
self.to_out = nn.Conv2d(hidden_dim, dim, 1, pad_mode='valid', has_bias=True)
self.map = ops.Map()
self.partial = ops.Partial()
def construct(self, x):
b, _, h, w = x.shape
qkv = self.to_qkv(x).chunk(3, 1)
q, k, v = self.map(self.partial(rearrange, self.heads), qkv)
q = q * self.scale
# 'b h d i, b h d j -> b h i j'
sim = ops.bmm(q.swapaxes(2, 3), k)
attn = ops.softmax(sim, axis=-1)
# 'b h i j, b h d j -> b h i d'
out = ops.bmm(attn, v.swapaxes(2, 3))
out = out.swapaxes(-1, -2).reshape((b, -1, h, w))
return self.to_out(out)
class LayerNorm(nn.Cell):
def __init__(self, dim):
super().__init__()
self.g = Parameter(initializer('ones', (1, dim, 1, 1)), name='g')
def construct(self, x):
eps = 1e-5
var = x.var(1, keepdims=True)
mean = x.mean(1, keep_dims=True)
return (x - mean) * rsqrt((var + eps)) * self.g
class LinearAttention(nn.Cell):
def __init__(self, dim, heads=4, dim_head=32):
super().__init__()
self.scale = dim_head ** -0.5
self.heads = heads
hidden_dim = dim_head * heads
self.to_qkv = nn.Conv2d(dim, hidden_dim * 3, 1, pad_mode='valid', has_bias=False)
self.to_out = nn.SequentialCell(
nn.Conv2d(hidden_dim, dim, 1, pad_mode='valid', has_bias=True),
LayerNorm(dim)
)
self.map = ops.Map()
self.partial = ops.Partial()
def construct(self, x):
b, _, h, w = x.shape
qkv = self.to_qkv(x).chunk(3, 1)
q, k, v = self.map(self.partial(rearrange, self.heads), qkv)
q = ops.softmax(q, -2)
k = ops.softmax(k, -1)
q = q * self.scale
v = v / (h * w)
# 'b h d n, b h e n -> b h d e'
context = ops.bmm(k, v.swapaxes(2, 3))
# 'b h d e, b h d n -> b h e n'
out = ops.bmm(context.swapaxes(2, 3), q)
out = out.reshape((b, -1, h, w))
return self.to_out(out)
2.5 组归一化
class PreNorm(nn.Cell):
def __init__(self, dim, fn):
super().__init__()
self.fn = fn
self.norm = nn.GroupNorm(1, dim)
def construct(self, x):
x = self.norm(x)
return self.fn(x)
2.6 条件U-Net
已经定义了所有的构建块（位置嵌入、ResNet/ConvNeXT块、Attention和组归一化），现在需要定义整个神经网络了。
网络构建过程如下：
- 首先，将卷积层应用于噪声图像批上，并计算噪声水平的位置
- 接下来，应用一系列下采样级。每个下采样阶段由2个ResNet/ConvNeXT块 + groupnorm + attention + 残差连接 + 一个下采样操作组成
- 在网络的中间，再次应用ResNet或ConvNeXT块，并与attention交织
- 接下来，应用一系列上采样级。每个上采样级由2个ResNet/ConvNeXT块+ groupnorm + attention + 残差连接 + 一个上采样操作组成
- 最后，应用ResNet/ConvNeXT块，然后应用卷积层
最终，神经网络将层堆叠起来
class Unet(nn.Cell):
def __init__(
self,
dim,
init_dim=None,
out_dim=None,
dim_mults=(1, 2, 4, 8),
channels=3,
with_time_emb=True,
convnext_mult=2,
):
super().__init__()
self.channels = channels
init_dim = default(init_dim, dim // 3 * 2)
self.init_conv = nn.Conv2d(channels, init_dim, 7, padding=3, pad_mode="pad", has_bias=True)
dims = [init_dim, *map(lambda m: dim * m, dim_mults)]
in_out = list(zip(dims[:-1], dims[1:]))
block_klass = partial(ConvNextBlock, mult=convnext_mult)
if with_time_emb:
time_dim = dim * 4
self.time_mlp = nn.SequentialCell(
SinusoidalPositionEmbeddings(dim),
nn.Dense(dim, time_dim),
nn.GELU(),
nn.Dense(time_dim, time_dim),
)
else:
time_dim = None
self.time_mlp = None
self.downs = nn.CellList([])
self.ups = nn.CellList([])
num_resolutions = len(in_out)
for ind, (dim_in, dim_out) in enumerate(in_out):
is_last = ind >= (num_resolutions - 1)
self.downs.append(
nn.CellList(
[
block_klass(dim_in, dim_out, time_emb_dim=time_dim),
block_klass(dim_out, dim_out, time_emb_dim=time_dim),
Residual(PreNorm(dim_out, LinearAttention(dim_out))),
Downsample(dim_out) if not is_last else nn.Identity(),
]
)
)
mid_dim = dims[-1]
self.mid_block1 = block_klass(mid_dim, mid_dim, time_emb_dim=time_dim)
self.mid_attn = Residual(PreNorm(mid_dim, Attention(mid_dim)))
self.mid_block2 = block_klass(mid_dim, mid_dim, time_emb_dim=time_dim)
for ind, (dim_in, dim_out) in enumerate(reversed(in_out[1:])):
is_last = ind >= (num_resolutions - 1)
self.ups.append(
nn.CellList(
[
block_klass(dim_out * 2, dim_in, time_emb_dim=time_dim),
block_klass(dim_in, dim_in, time_emb_dim=time_dim),
Residual(PreNorm(dim_in, LinearAttention(dim_in))),
Upsample(dim_in) if not is_last else nn.Identity(),
]
)
)
out_dim = default(out_dim, channels)
self.final_conv = nn.SequentialCell(
block_klass(dim, dim), nn.Conv2d(dim, out_dim, 1)
)
def construct(self, x, time):
x = self.init_conv(x)
t = self.time_mlp(time) if exists(self.time_mlp) else None
h = []
for block1, block2, attn, downsample in self.downs:
x = block1(x, t)
x = block2(x, t)
x = attn(x)
h.append(x)
x = downsample(x)
x = self.mid_block1(x, t)
x = self.mid_attn(x)
x = self.mid_block2(x, t)
len_h = len(h) - 1
for block1, block2, attn, upsample in self.ups:
x = ops.concat((x, h[len_h]), 1)
len_h -= 1
x = block1(x, t)
x = block2(x, t)
x = attn(x)
x = upsample(x)
return self.final_conv(x)
2.6 正向扩散
定义T时间步的时间表
def linear_beta_schedule(timesteps):
beta_start = 0.0001
beta_end = 0.02
return np.linspace(beta_start, beta_end, timesteps).astype(np.float32)
# 扩散200步
timesteps = 200
# 定义 beta schedule
betas = linear_beta_schedule(timesteps=timesteps)
# 定义 alphas
alphas = 1. - betas
alphas_cumprod = np.cumprod(alphas, axis=0)
alphas_cumprod_prev = np.pad(alphas_cumprod[:-1], (1, 0), constant_values=1)
sqrt_recip_alphas = Tensor(np.sqrt(1. / alphas))
sqrt_alphas_cumprod = Tensor(np.sqrt(alphas_cumprod))
sqrt_one_minus_alphas_cumprod = Tensor(np.sqrt(1. - alphas_cumprod))
# 计算 q(x_{t-1} | x_t, x_0)
posterior_variance = betas * (1. - alphas_cumprod_prev) / (1. - alphas_cumprod)
p2_loss_weight = (1 + alphas_cumprod / (1 - alphas_cumprod)) ** -0.
p2_loss_weight = Tensor(p2_loss_weight)
def extract(a, t, x_shape):
b = t.shape[0]
out = Tensor(a).gather(t, -1)
return out.reshape(b, *((1,) * (len(x_shape) - 1)))
测试将猫图像在扩散过程的每个时间步骤中添加噪音
from PIL import Image
image = Image.open('./image_cat/jpg/000000039769.jpg')
base_width = 160
image = image.resize((base_width, int(float(image.size[1]) * float(base_width / float(image.size[0])))))
image.show()
噪声被添加到mindspore张量中，而不是Pillow图像。我们将首先定义图像转换，允许我们从PIL图像转换到mindspore张量（我们可以在其上添加噪声），反之亦然。
这些转换相当简单：我们首先通过除以255来标准化图像（使它们在 [0,1] 范围内），然后确保它们在 [-1,1]范围内。
from mindspore.dataset import ImageFolderDataset
image_size = 128
transforms = [
Resize(image_size, Inter.BILINEAR),
CenterCrop(image_size),
ToTensor(),
lambda t: (t * 2) - 1
]
path = './image_cat'
dataset = ImageFolderDataset(dataset_dir=path, num_parallel_workers=cpu_count(),
extensions=['.jpg', '.jpeg', '.png', '.tiff'],
num_shards=1, shard_id=0, shuffle=False, decode=True)
dataset = dataset.project('image')
transforms.insert(1, RandomHorizontalFlip())
dataset_1 = dataset.map(transforms, 'image')
dataset_2 = dataset_1.batch(1, drop_remainder=True)
x_start = next(dataset_2.create_tuple_iterator())[0]
print(x_start.shape)
shape:(1, 3, 128, 128)
定义反向变换，它接收一个包含 [-1,1]中的张量，并将它们转回 PIL 图像.
import numpy as np
reverse_transform = [
lambda t: (t + 1) / 2,
lambda t: ops.permute(t, (1, 2, 0)), # CHW to HWC
lambda t: t * 255.,
lambda t: t.asnumpy().astype(np.uint8),
ToPIL()
]
def compose(transform, x):
for d in transform:
x = d(x)
return x
定义前向扩散过程
def q_sample(x_start, t, noise=None):
if noise is None:
noise = randn_like(x_start)
return (extract(sqrt_alphas_cumprod, t, x_start.shape) * x_start +
extract(sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise)
在特定的时间步长上测试:
def get_noisy_image(x_start, t):
# 添加噪音
x_noisy = q_sample(x_start, t=t)
# 转换为 PIL 图像
noisy_image = compose(reverse_transform, x_noisy[0])
return noisy_image
# 设置 time step
t = Tensor([40])
noisy_image = get_noisy_image(x_start, t)
print(noisy_image)
noisy_image.show()
为不同的时间步骤可视化此情况：
import matplotlib.pyplot as plt
def plot(imgs, with_orig=False, row_title=None, **imshow_kwargs):
if not isinstance(imgs[0], list):
imgs = [imgs]
num_rows = len(imgs)
num_cols = len(imgs[0]) + with_orig
_, axs = plt.subplots(figsize=(200, 200), nrows=num_rows, ncols=num_cols, squeeze=False)
for row_idx, row in enumerate(imgs):
row = [image] + row if with_orig else row
for col_idx, img in enumerate(row):
ax = axs[row_idx, col_idx]
ax.imshow(np.asarray(img), **imshow_kwargs)
ax.set(xticklabels=[], yticklabels=[], xticks=[], yticks=[])
if with_orig:
axs[0, 0].set(title='Original image')
axs[0, 0].title.set_size(8)
if row_title is not None:
for row_idx in range(num_rows):
axs[row_idx, 0].set(ylabel=row_title[row_idx])
plt.tight_layout()
测试：plot([get_noisy_image(x_start, Tensor([t])) for t in [0, 50, 100, 150, 199]])
2.7 定义给定模型的损失函数
denoise_model将是定义的U-Net。我们将在真实噪声和预测噪声之间使用Huber损失。
def p_losses(unet_model, x_start, t, noise=None):
if noise is None:
noise = randn_like(x_start)
x_noisy = q_sample(x_start=x_start, t=t, noise=noise)
predicted_noise = unet_model(x_noisy, t)
loss = nn.SmoothL1Loss()(noise, predicted_noise)# todo
loss = loss.reshape(loss.shape[0], -1)
loss = loss * extract(p2_loss_weight, t, loss.shape)
return loss.mean()
下一章：数据集准备与处理
