Diffusion Model Variational Lower Bound Loss
Tags: #machine learning #diffusionEquation
$$\begin{aligned} L_\text{VLB} &= L_T + L_{T-1} + \dots + L_0 \\ \text{where } L_T &= D_\text{KL}(q(\mathbf{x}_T \vert \mathbf{x}_0) \parallel p_\theta(\mathbf{x}_T)) \\ L_t &= D_\text{KL}(q(\mathbf{x}_t \vert \mathbf{x}_{t+1}, \mathbf{x}_0) \parallel p_\theta(\mathbf{x}_t \vert\mathbf{x}_{t+1})) \text{ for }1 \leq t \leq T-1 \\ L_0 &= - \log p_\theta(\mathbf{x}_0 \vert \mathbf{x}_1) \end{aligned}$$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
Related Documents
- Latex Code for Diffusion Models Equations
- Weng, Lilian. (Jul 2021). What are diffusion models? Lil'Log.
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