A question about "a[t - 1, x, :]" about d3pm

[qixuema]

Hi @QWTforGithub , the x_0 in the paper is a one-hot row vector. When x_0 multiplies with Q_t in the formula, in the code, it effectively acts as indexing from the corresponding position in Q_t, I guess that's how it works.

I've also been following d3pm recently, feel free to reach out for discussion anytime.

[QWTforGithub]

Hi @QWTforGithub , the x_0 in the paper is a one-hot row vector. When x_0 multiplies with Q_t in the formula, in the code, it effectively acts as indexing from the corresponding position in Q_t, I guess that's how it works.

I've also been following d3pm recently, feel free to reach out for discussion anytime.

Thank you for your reply. Now I have another question about "vb loss":

**def vb(self, dist1, dist2):

    # flatten dist1 and dist2
    dist1 = dist1.flatten(start_dim=0, end_dim=-2)
    dist2 = dist2.flatten(start_dim=0, end_dim=-2)

    out = torch.softmax(dist1 + self.eps, dim=-1) * (
        torch.log_softmax(dist1 + self.eps, dim=-1)
        - torch.log_softmax(dist2 + self.eps, dim=-1)
    )
    return out.sum(dim=-1).mean()**

My understanding of "vb loss" is "Variational Bayes Loss", that is, an MSE loss + a KL divergence. (torch.log_softmax(dist1 + self.eps, dim=-1) - torch.log_softmax(dist2 + self.eps, dim=-1))" can be considered as the difference of two posterior distributions (a KL divergence). But, why should What about multiplying by "torch.softmax(dist1 + self.eps, dim=-1)"? Looking forward to your reply.

[qixuema]

@QWTforGithub I feel that this should just be a simple calculation of the KL divergence loss.

$$ L(y_{pred}, y_{true}) = y_{true} \cdot \log \frac{y_{true}}{y_{pred}} = y_{true} \cdot (\log y_{true} - \log y_{pred}) $$

I feel that the step 'torch.softmax(dist1 + self.eps, dim=-1)' is just converting dist1 from logits to probabilities.

[QWTforGithub]

@QWTforGithub I feel that this should just be a simple calculation of the KL divergence loss.

L(ypred,ytrue)=ytrue⋅log⁡ytrueypred=ytrue⋅(log⁡ytrue−log⁡ypred)

I feel that the step 'torch.softmax(dist1 + self.eps, dim=-1)' is just converting dist1 from logits to probabilities.

Thank you very much for your answer! May I ask you have tried to derive the formula in D3PM (Eq 3)? Why does the posterior distribution q(xt-1|xt,x0) get the form of Eq3? This transition probability p:
$$(x_tQ_t^T * x_0\bar{Q_{t-1}})/x_0\bar{Q_t}x^T$$
But not:
$$(x_{t-1}Q_t * x_0\bar{Q}_{t-1})/x_0\bar{Q}_t$$
How is Eq3 derived?

[qixuema]

@QWTforGithub Sorry, I feel it's a bit inappropriate to discuss here. I haven't found your email yet. If you don't mind, we can discuss on WeChat or elsewhere. Here's my email: [email protected].

[QWTforGithub]

@QWTforGithub Sorry, I feel it's a bit inappropriate to discuss here. I haven't found your email yet. If you don't mind, we can discuss on WeChat or elsewhere. Here's my email: [email protected].

Thank you very much. I have sent a message to your email. I hope to communicate with you further.