SDE
A differential equation describing the evolution of stochastic dynamical systems, comprising a deterministic drift term and a stochastic diffusion term.
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When the step size $\eta \to 0$, the trajectory of the SGD iteration $x_{k+1} = x_k - \eta \nabla f(x_k) + \eta \xi_k$ can be approximated by an SDE: $dX_t = -\nabla f(X_t)\,dt + \sqrt{\eta}\,\Sigma\,dW_t$.
The general form of a stochastic differential equation is dX = f(X,t)dt + g(X,t)dW, where f is the drift term and g is the diffusion term.
The choice of sampler has a pivotal impact on the final quality of diffusion model inference; common samplers include Euler, DPM++, DDIM, and the SDE series, which are essentially different numerical solving strategies for stochastic or ordinary differential equations.
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When the step size $\eta \to 0$, the trajectory of the SGD iteration $x_{k+1} = x_k - \eta \nabla f(x_k) + \eta \xi_k$ can be approximated by an SDE: $dX_t = -\nabla f(X_t)\,dt + \sqrt{\eta}\,\Sigma\,dW_t$.
50%UnverifiedThe general form of a stochastic differential equation is dX = f(X,t)dt + g(X,t)dW, where f is the drift term and g is the diffusion term.
50%UnverifiedThe choice of sampler has a pivotal impact on the final quality of diffusion model inference; common samplers include Euler, DPM++, DDIM, and the SDE series, which are essentially different numerical solving strategies for stochastic or ordinary differential equations.
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