File size: 11,888 Bytes
bf8981a
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
"""
---
title: Transformer for Stable Diffusion U-Net
summary: >
 Annotated PyTorch implementation/tutorial of the transformer
 for U-Net in stable diffusion.
---

# Transformer for Stable Diffusion [U-Net](unet.html)

This implements the transformer module used in [U-Net](unet.html) that
 gives $\epsilon_\text{cond}(x_t, c)$

We have kept to the model definition and naming unchanged from
[CompVis/stable-diffusion](https://github.com/CompVis/stable-diffusion)
so that we can load the checkpoints directly.
"""

from typing import Optional

import torch
import torch.nn.functional as F
from torch import nn


class SpatialTransformer(nn.Module):
    """
    ## Spatial Transformer
    """
    def __init__(self, channels: int, n_heads: int, n_layers: int):
        """
        :param channels: is the number of channels in the feature map
        :param n_heads: is the number of attention heads
        :param n_layers: is the number of transformer layers
        :param d_cond: is the size of the conditional embedding
        """
        super().__init__()
        # Initial group normalization
        self.norm = torch.nn.GroupNorm(
            num_groups=32, num_channels=channels, eps=1e-6, affine=True
        )
        # Initial $1 \times 1$ convolution
        self.proj_in = nn.Conv2d(channels, channels, kernel_size=1, stride=1, padding=0)

        # Transformer layers
        self.transformer_blocks = nn.ModuleList(
            [
                BasicTransformerBlock(
                    channels, n_heads, channels // n_heads
                ) for _ in range(n_layers)
            ]
        )

        # Final $1 \times 1$ convolution
        self.proj_out = nn.Conv2d(
            channels, channels, kernel_size=1, stride=1, padding=0
        )

    def forward(self, x: torch.Tensor):
        """
        :param x: is the feature map of shape `[batch_size, channels, height, width]`
        :param cond: is the conditional embeddings of shape `[batch_size,  n_cond, d_cond]`
        """
        # Get shape `[batch_size, channels, height, width]`
        b, c, h, w = x.shape
        # For residual connection
        x_in = x
        # Normalize
        x = self.norm(x)
        # Initial $1 \times 1$ convolution
        x = self.proj_in(x)
        # Transpose and reshape from `[batch_size, channels, height, width]`
        # to `[batch_size, height * width, channels]`
        x = x.permute(0, 2, 3, 1).view(b, h * w, c)
        # Apply the transformer layers
        for block in self.transformer_blocks:
            x = block(x)
        # Reshape and transpose from `[batch_size, height * width, channels]`
        # to `[batch_size, channels, height, width]`
        x = x.view(b, h, w, c).permute(0, 3, 1, 2)
        # Final $1 \times 1$ convolution
        x = self.proj_out(x)
        # Add residual
        return x + x_in


class BasicTransformerBlock(nn.Module):
    """
    ### Transformer Layer
    """
    def __init__(self, d_model: int, n_heads: int, d_head: int):
        """
        :param d_model: is the input embedding size
        :param n_heads: is the number of attention heads
        :param d_head: is the size of a attention head
        :param d_cond: is the size of the conditional embeddings
        """
        super().__init__()
        # Self-attention layer and pre-norm layer
        self.attn1 = CrossAttention(d_model, d_model, n_heads, d_head)
        self.norm1 = nn.LayerNorm(d_model)
        # Cross attention layer and pre-norm layer
        #self.attn2 = CrossAttention(d_model, d_cond, n_heads, d_head)
        self.norm2 = nn.LayerNorm(d_model)
        # Feed-forward network and pre-norm layer
        self.ff = FeedForward(d_model)
        self.norm3 = nn.LayerNorm(d_model)

    def forward(self, x: torch.Tensor):
        """
        :param x: are the input embeddings of shape `[batch_size, height * width, d_model]`
        :param cond: is the conditional embeddings of shape `[batch_size,  n_cond, d_cond]`
        """
        # Self attention
        x = self.attn1(self.norm1(x)) + x
        # Cross-attention with conditioning
        # x = self.attn2(self.norm2(x), cond=cond) + x
        # Feed-forward network
        x = self.ff(self.norm3(x)) + x
        #
        return x


class CrossAttention(nn.Module):
    """
    ### Cross Attention Layer

    This falls-back to self-attention when conditional embeddings are not specified.
    """

    use_flash_attention: bool = False

    def __init__(
        self,
        d_model: int,
        d_cond: int,
        n_heads: int,
        d_head: int,
        is_inplace: bool = True
    ):
        """
        :param d_model: is the input embedding size
        :param n_heads: is the number of attention heads
        :param d_head: is the size of a attention head
        :param d_cond: is the size of the conditional embeddings
        :param is_inplace: specifies whether to perform the attention softmax computation inplace to
            save memory
        """
        super().__init__()

        self.is_inplace = is_inplace
        self.n_heads = n_heads
        self.d_head = d_head

        # Attention scaling factor
        self.scale = d_head**-0.5

        # Query, key and value mappings
        d_attn = d_head * n_heads
        self.to_q = nn.Linear(d_model, d_attn, bias=False)
        self.to_k = nn.Linear(d_cond, d_attn, bias=False)
        self.to_v = nn.Linear(d_cond, d_attn, bias=False)

        # Final linear layer
        self.to_out = nn.Sequential(nn.Linear(d_attn, d_model))

        # Setup [flash attention](https://github.com/HazyResearch/flash-attention).
        # Flash attention is only used if it's installed
        # and `CrossAttention.use_flash_attention` is set to `True`.
        try:
            # You can install flash attention by cloning their Github repo,
            # [https://github.com/HazyResearch/flash-attention](https://github.com/HazyResearch/flash-attention)
            # and then running `python setup.py install`
            from flash_attn.flash_attention import FlashAttention
            self.flash = FlashAttention()
            # Set the scale for scaled dot-product attention.
            self.flash.softmax_scale = self.scale
        # Set to `None` if it's not installed
        except ImportError:
            self.flash = None

    def forward(self, x: torch.Tensor, cond: Optional[torch.Tensor] = None):
        """
        :param x: are the input embeddings of shape `[batch_size, height * width, d_model]`
        :param cond: is the conditional embeddings of shape `[batch_size, n_cond, d_cond]`
        """

        # If `cond` is `None` we perform self attention
        has_cond = cond is not None
        if not has_cond:
            cond = x

        # Get query, key and value vectors
        q = self.to_q(x)
        k = self.to_k(cond)
        v = self.to_v(cond)

        # Use flash attention if it's available and the head size is less than or equal to `128`
        if CrossAttention.use_flash_attention and self.flash is not None and not has_cond and self.d_head <= 128:
            return self.flash_attention(q, k, v)
        # Otherwise, fallback to normal attention
        else:
            return self.normal_attention(q, k, v)

    def flash_attention(self, q: torch.Tensor, k: torch.Tensor, v: torch.Tensor):
        """
        #### Flash Attention

        :param q: are the query vectors before splitting heads, of shape `[batch_size, seq, d_attn]`
        :param k: are the query vectors before splitting heads, of shape `[batch_size, seq, d_attn]`
        :param v: are the query vectors before splitting heads, of shape `[batch_size, seq, d_attn]`
        """

        # Get batch size and number of elements along sequence axis (`width * height`)
        batch_size, seq_len, _ = q.shape

        # Stack `q`, `k`, `v` vectors for flash attention, to get a single tensor of
        # shape `[batch_size, seq_len, 3, n_heads * d_head]`
        qkv = torch.stack((q, k, v), dim=2)
        # Split the heads
        qkv = qkv.view(batch_size, seq_len, 3, self.n_heads, self.d_head)

        # Flash attention works for head sizes `32`, `64` and `128`, so we have to pad the heads to
        # fit this size.
        if self.d_head <= 32:
            pad = 32 - self.d_head
        elif self.d_head <= 64:
            pad = 64 - self.d_head
        elif self.d_head <= 128:
            pad = 128 - self.d_head
        else:
            raise ValueError(f'Head size ${self.d_head} too large for Flash Attention')

        # Pad the heads
        if pad:
            qkv = torch.cat(
                (qkv, qkv.new_zeros(batch_size, seq_len, 3, self.n_heads, pad)), dim=-1
            )

        # Compute attention
        # $$\underset{seq}{softmax}\Bigg(\frac{Q K^\top}{\sqrt{d_{key}}}\Bigg)V$$
        # This gives a tensor of shape `[batch_size, seq_len, n_heads, d_padded]`
        out, _ = self.flash(qkv)
        # Truncate the extra head size
        out = out[:, :, :, : self.d_head]
        # Reshape to `[batch_size, seq_len, n_heads * d_head]`
        out = out.reshape(batch_size, seq_len, self.n_heads * self.d_head)

        # Map to `[batch_size, height * width, d_model]` with a linear layer
        return self.to_out(out)

    def normal_attention(self, q: torch.Tensor, k: torch.Tensor, v: torch.Tensor):
        """
        #### Normal Attention
        
        :param q: are the query vectors before splitting heads, of shape `[batch_size, seq, d_attn]`
        :param k: are the query vectors before splitting heads, of shape `[batch_size, seq, d_attn]`
        :param v: are the query vectors before splitting heads, of shape `[batch_size, seq, d_attn]`
        """

        # Split them to heads of shape `[batch_size, seq_len, n_heads, d_head]`
        q = q.view(*q.shape[: 2], self.n_heads, -1)
        k = k.view(*k.shape[: 2], self.n_heads, -1)
        v = v.view(*v.shape[: 2], self.n_heads, -1)

        # Calculate attention $\frac{Q K^\top}{\sqrt{d_{key}}}$
        attn = torch.einsum('bihd,bjhd->bhij', q, k) * self.scale

        # Compute softmax
        # $$\underset{seq}{softmax}\Bigg(\frac{Q K^\top}{\sqrt{d_{key}}}\Bigg)$$
        if self.is_inplace:
            half = attn.shape[0] // 2
            attn[half :] = attn[half :].softmax(dim=-1)
            attn[: half] = attn[: half].softmax(dim=-1)
        else:
            attn = attn.softmax(dim=-1)

        # Compute attention output
        # $$\underset{seq}{softmax}\Bigg(\frac{Q K^\top}{\sqrt{d_{key}}}\Bigg)V$$
        out = torch.einsum('bhij,bjhd->bihd', attn, v)
        # Reshape to `[batch_size, height * width, n_heads * d_head]`
        out = out.reshape(*out.shape[: 2], -1)
        # Map to `[batch_size, height * width, d_model]` with a linear layer
        return self.to_out(out)


class FeedForward(nn.Module):
    """
    ### Feed-Forward Network
    """
    def __init__(self, d_model: int, d_mult: int = 4):
        """
        :param d_model: is the input embedding size
        :param d_mult: is multiplicative factor for the hidden layer size
        """
        super().__init__()
        self.net = nn.Sequential(
            GeGLU(d_model, d_model * d_mult), nn.Dropout(0.),
            nn.Linear(d_model * d_mult, d_model)
        )

    def forward(self, x: torch.Tensor):
        return self.net(x)


class GeGLU(nn.Module):
    """
    ### GeGLU Activation

    $$\text{GeGLU}(x) = (xW + b) * \text{GELU}(xV + c)$$
    """
    def __init__(self, d_in: int, d_out: int):
        super().__init__()
        # Combined linear projections $xW + b$ and $xV + c$
        self.proj = nn.Linear(d_in, d_out * 2)

    def forward(self, x: torch.Tensor):
        # Get $xW + b$ and $xV + c$
        x, gate = self.proj(x).chunk(2, dim=-1)
        # $\text{GeGLU}(x) = (xW + b) * \text{GELU}(xV + c)$
        return x * F.gelu(gate)