Diffusion Model Variational Lower Bound Loss

Tags: #machine learning #diffusion

Equation

$$\begin{aligned} L_\text{VLB} &= L_T + L_{T-1} + \dots + L_0 \\ \text{where } L_T &= D_\text{KL}(q(\mathbf{x}_T \vert \mathbf{x}_0) \parallel p_\theta(\mathbf{x}_T)) \\ L_t &= D_\text{KL}(q(\mathbf{x}_t \vert \mathbf{x}_{t+1}, \mathbf{x}_0) \parallel p_\theta(\mathbf{x}_t \vert\mathbf{x}_{t+1})) \text{ for }1 \leq t \leq T-1 \\ L_0 &= - \log p_\theta(\mathbf{x}_0 \vert \mathbf{x}_1) \end{aligned}$$

Latex Code

                                 \begin{aligned}
            L_\text{VLB} &= L_T + L_{T-1} + \dots + L_0 \\
            \text{where } L_T &= D_\text{KL}(q(\mathbf{x}_T \vert \mathbf{x}_0) \parallel p_\theta(\mathbf{x}_T)) \\
            L_t &= D_\text{KL}(q(\mathbf{x}_t \vert \mathbf{x}_{t+1}, \mathbf{x}_0) \parallel p_\theta(\mathbf{x}_t \vert\mathbf{x}_{t+1})) \text{ for }1 \leq t \leq T-1 \\
            L_0 &= - \log p_\theta(\mathbf{x}_0 \vert \mathbf{x}_1)
            \end{aligned}
                            

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Introduction

Equation



Latex Code

            \begin{aligned}
            L_\text{VLB} &= L_T + L_{T-1} + \dots + L_0 \\
            \text{where } L_T &= D_\text{KL}(q(\mathbf{x}_T \vert \mathbf{x}_0) \parallel p_\theta(\mathbf{x}_T)) \\
            L_t &= D_\text{KL}(q(\mathbf{x}_t \vert \mathbf{x}_{t+1}, \mathbf{x}_0) \parallel p_\theta(\mathbf{x}_t \vert\mathbf{x}_{t+1})) \text{ for }1 \leq t \leq T-1 \\
            L_0 &= - \log p_\theta(\mathbf{x}_0 \vert \mathbf{x}_1)
            \end{aligned}
        

Explanation

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