File size: 7,977 Bytes
753e275
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F

from diffab.modules.common.layers import clampped_one_hot
from diffab.modules.common.so3 import ApproxAngularDistribution, random_normal_so3, so3vec_to_rotation, rotation_to_so3vec


class VarianceSchedule(nn.Module):

    def __init__(self, num_steps=100, s=0.01):
        super().__init__()
        T = num_steps
        t = torch.arange(0, num_steps+1, dtype=torch.float)
        f_t = torch.cos( (np.pi / 2) * ((t/T) + s) / (1 + s) ) ** 2
        alpha_bars = f_t / f_t[0]

        betas = 1 - (alpha_bars[1:] / alpha_bars[:-1])
        betas = torch.cat([torch.zeros([1]), betas], dim=0)
        betas = betas.clamp_max(0.999)

        sigmas = torch.zeros_like(betas)
        for i in range(1, betas.size(0)):
            sigmas[i] = ((1 - alpha_bars[i-1]) / (1 - alpha_bars[i])) * betas[i]
        sigmas = torch.sqrt(sigmas)

        self.register_buffer('betas', betas)
        self.register_buffer('alpha_bars', alpha_bars)
        self.register_buffer('alphas', 1 - betas)
        self.register_buffer('sigmas', sigmas)


class PositionTransition(nn.Module):

    def __init__(self, num_steps, var_sched_opt={}):
        super().__init__()
        self.var_sched = VarianceSchedule(num_steps, **var_sched_opt)

    def add_noise(self, p_0, mask_generate, t):
        """
        Args:
            p_0:    (N, L, 3).
            mask_generate:    (N, L).
            t:  (N,).
        """
        alpha_bar = self.var_sched.alpha_bars[t]

        c0 = torch.sqrt(alpha_bar).view(-1, 1, 1)
        c1 = torch.sqrt(1 - alpha_bar).view(-1, 1, 1)

        e_rand = torch.randn_like(p_0)
        p_noisy = c0*p_0 + c1*e_rand
        p_noisy = torch.where(mask_generate[..., None].expand_as(p_0), p_noisy, p_0)

        return p_noisy, e_rand

    def denoise(self, p_t, eps_p, mask_generate, t):
        # IMPORTANT:
        #   clampping alpha is to fix the instability issue at the first step (t=T)
        #   it seems like a problem with the ``improved ddpm''.
        alpha = self.var_sched.alphas[t].clamp_min(
            self.var_sched.alphas[-2]
        )
        alpha_bar = self.var_sched.alpha_bars[t]
        sigma = self.var_sched.sigmas[t].view(-1, 1, 1)

        c0 = ( 1.0 / torch.sqrt(alpha + 1e-8) ).view(-1, 1, 1)
        c1 = ( (1 - alpha) / torch.sqrt(1 - alpha_bar + 1e-8) ).view(-1, 1, 1)

        z = torch.where(
            (t > 1)[:, None, None].expand_as(p_t),
            torch.randn_like(p_t),
            torch.zeros_like(p_t),
        )

        p_next = c0 * (p_t - c1 * eps_p) + sigma * z
        p_next = torch.where(mask_generate[..., None].expand_as(p_t), p_next, p_t)
        return p_next


class RotationTransition(nn.Module):

    def __init__(self, num_steps, var_sched_opt={}, angular_distrib_fwd_opt={}, angular_distrib_inv_opt={}):
        super().__init__()
        self.var_sched = VarianceSchedule(num_steps, **var_sched_opt)

        # Forward (perturb)
        c1 = torch.sqrt(1 - self.var_sched.alpha_bars) # (T,).
        self.angular_distrib_fwd = ApproxAngularDistribution(c1.tolist(), **angular_distrib_fwd_opt)

        # Inverse (generate)
        sigma = self.var_sched.sigmas
        self.angular_distrib_inv = ApproxAngularDistribution(sigma.tolist(), **angular_distrib_inv_opt)

        self.register_buffer('_dummy', torch.empty([0, ]))

    def add_noise(self, v_0, mask_generate, t):
        """
        Args:
            v_0:    (N, L, 3).
            mask_generate:    (N, L).
            t:  (N,).
        """
        N, L = mask_generate.size()
        alpha_bar = self.var_sched.alpha_bars[t]
        c0 = torch.sqrt(alpha_bar).view(-1, 1, 1)
        c1 = torch.sqrt(1 - alpha_bar).view(-1, 1, 1)

        # Noise rotation
        e_scaled = random_normal_so3(t[:, None].expand(N, L), self.angular_distrib_fwd, device=self._dummy.device)    # (N, L, 3)
        e_normal = e_scaled / (c1 + 1e-8)
        E_scaled = so3vec_to_rotation(e_scaled)   # (N, L, 3, 3)

        # Scaled true rotation
        R0_scaled = so3vec_to_rotation(c0 * v_0)  # (N, L, 3, 3)

        R_noisy = E_scaled @ R0_scaled
        v_noisy = rotation_to_so3vec(R_noisy)
        v_noisy = torch.where(mask_generate[..., None].expand_as(v_0), v_noisy, v_0)

        return v_noisy, e_scaled

    def denoise(self, v_t, v_next, mask_generate, t):
        N, L = mask_generate.size()
        e = random_normal_so3(t[:, None].expand(N, L), self.angular_distrib_inv, device=self._dummy.device) # (N, L, 3)
        e = torch.where(
            (t > 1)[:, None, None].expand(N, L, 3),
            e, 
            torch.zeros_like(e) # Simply denoise and don't add noise at the last step
        )
        E = so3vec_to_rotation(e)

        R_next = E @ so3vec_to_rotation(v_next)
        v_next = rotation_to_so3vec(R_next)
        v_next = torch.where(mask_generate[..., None].expand_as(v_next), v_next, v_t)

        return v_next


class AminoacidCategoricalTransition(nn.Module):
    
    def __init__(self, num_steps, num_classes=20, var_sched_opt={}):
        super().__init__()
        self.num_classes = num_classes
        self.var_sched = VarianceSchedule(num_steps, **var_sched_opt)

    @staticmethod
    def _sample(c):
        """
        Args:
            c:    (N, L, K).
        Returns:
            x:    (N, L).
        """
        N, L, K = c.size()
        c = c.view(N*L, K) + 1e-8
        x = torch.multinomial(c, 1).view(N, L)
        return x

    def add_noise(self, x_0, mask_generate, t):
        """
        Args:
            x_0:    (N, L)
            mask_generate:    (N, L).
            t:  (N,).
        Returns:
            c_t:    Probability, (N, L, K).
            x_t:    Sample, LongTensor, (N, L).
        """
        N, L = x_0.size()
        K = self.num_classes
        c_0 = clampped_one_hot(x_0, num_classes=K).float() # (N, L, K).
        alpha_bar = self.var_sched.alpha_bars[t][:, None, None] # (N, 1, 1)
        c_noisy = (alpha_bar*c_0) + ( (1-alpha_bar)/K )
        c_t = torch.where(mask_generate[..., None].expand(N,L,K), c_noisy, c_0)
        x_t = self._sample(c_t)
        return c_t, x_t

    def posterior(self, x_t, x_0, t):
        """
        Args:
            x_t:    Category LongTensor (N, L) or Probability FloatTensor (N, L, K).
            x_0:    Category LongTensor (N, L) or Probability FloatTensor (N, L, K).
            t:  (N,).
        Returns:
            theta:  Posterior probability at (t-1)-th step, (N, L, K).
        """
        K = self.num_classes

        if x_t.dim() == 3:
            c_t = x_t   # When x_t is probability distribution.
        else:
            c_t = clampped_one_hot(x_t, num_classes=K).float() # (N, L, K)

        if x_0.dim() == 3:
            c_0 = x_0   # When x_0 is probability distribution.
        else:
            c_0 = clampped_one_hot(x_0, num_classes=K).float() # (N, L, K)

        alpha = self.var_sched.alpha_bars[t][:, None, None]     # (N, 1, 1)
        alpha_bar = self.var_sched.alpha_bars[t][:, None, None] # (N, 1, 1)

        theta = ((alpha*c_t) + (1-alpha)/K) * ((alpha_bar*c_0) + (1-alpha_bar)/K)   # (N, L, K)
        theta = theta / (theta.sum(dim=-1, keepdim=True) + 1e-8)
        return theta

    def denoise(self, x_t, c_0_pred, mask_generate, t):
        """
        Args:
            x_t:        (N, L).
            c_0_pred:   Normalized probability predicted by networks, (N, L, K).
            mask_generate:    (N, L).
            t:  (N,).
        Returns:
            post:   Posterior probability at (t-1)-th step, (N, L, K).
            x_next: Sample at (t-1)-th step, LongTensor, (N, L).
        """
        c_t = clampped_one_hot(x_t, num_classes=self.num_classes).float()  # (N, L, K)
        post = self.posterior(c_t, c_0_pred, t=t)   # (N, L, K)
        post = torch.where(mask_generate[..., None].expand(post.size()), post, c_t)
        x_next = self._sample(post)
        return post, x_next