昇思MindSpore进阶教程--Diffusion扩散模型(中)

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构建Diffusion模型

下面，我们逐步构建Diffusion模型。

首先，我们定义了一些帮助函数和类，这些函数和类将在实现神经网络时使用。

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.')

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

我们还定义了上采样和下采样操作的别名。

def Upsample(dim):
    return nn.Conv2dTranspose(dim, dim, 4, 2, pad_mode="pad", padding=1)

def Downsample(dim):
    return nn.Conv2d(dim, dim, 4, 2, pad_mode="pad", padding=1)

位置向量

由于神经网络的参数在时间（噪声水平）上共享，作者使用正弦位置嵌入来编码
，灵感来自Transformer（Vaswani et al., 2017）。对于批处理中的每一张图像，神经网络“知道”它在哪个特定时间步长（噪声水平）上运行。

SinusoidalPositionEmbeddings模块采用(batch_size, 1)形状的张量作为输入（即批处理中几个有噪声图像的噪声水平），并将其转换为(batch_size, dim)形状的张量，其中dim是位置嵌入的尺寸。然后，我们将其添加到每个剩余块中。

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

ResNet/ConvNeXT块

接下来，我们定义U-Net模型的核心构建块。DDPM作者使用了一个Wide ResNet块（Zagoruyko et al., 2016），但Phil Wang决定添加ConvNeXT（Liu et al., 2022）替换ResNet，因为后者在图像领域取得了巨大成功。

在最终的U-Net架构中，可以选择其中一个或另一个，本文选择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)

Attention模块

接下来，我们定义Attention模块，DDPM作者将其添加到卷积块之间。Attention是著名的Transformer架构(Vaswani et al., 2017)，在人工智能的各个领域都取得了巨大的成功，从NLP到蛋白质折叠。Phil Wang使用了两种注意力变体：一种是常规的multi-head self-attention（如Transformer中使用的），另一种是LinearAttention(Shen et al., 2018)，其时间和内存要求在序列长度上线性缩放，而不是在常规注意力中缩放。 要想对Attention机制进行深入的了解，请参照Jay Allamar的精彩的博文。

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)

组归一化

DDPM作者将U-Net的卷积/注意层与群归一化（Wu et al., 2018）。下面，我们定义一个PreNorm类，将用于在注意层之前应用groupnorm。

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)

条件U-Net

我们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。请记住，网络
的工作是接收一批噪声图像+噪声水平，并输出添加到输入中的噪声。

更具体的： 网络获取了一批(batch_size, num_channels, height, width)形状的噪声图像和一批(batch_size, 1)形状的噪音水平作为输入，并返回(batch_size, num_channels, height, width)形状的张量。

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，就像它们是乐高积木一样（但重要的是了解它们是如何工作的）。

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)

正向扩散

我们已经知道正向扩散过程在多个时间步长T中，从实际分布逐渐向图像添加噪声，根据差异计划进行正向扩散。
下面，我们定义了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)