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A neural SDE refers to a class of models that parameterize the drift and/or diffusion terms of a stochastic differential equation with neural networks, with the standard form dX_t = f_θ(X_t, t)dt + g_φ(X_t, t)dW_t.
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11/2/2026
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UnverifiedA neural stochastic differential equation replaces the drift and diffusion terms in classical SDEs with neural networks, thereby modeling stochastic dynamic processes in continuous time.76% similarUnverifiedIn the DDPM reverse process, the mean μ_θ is expressed as μ_θ(x_t, t) = (1/√α_t) · (x_t - (β_t / √(1 - ᾱ_t)) · ε_θ(x_t, t)), where ε_θ is the neural network to be trained.69% similarUnverifiedThe differential neural tangent kernel (DNTK) characterizes the inner products of the gradients of a network's output and its derivatives with respect to the parameters.67% similarUnverifiedThe reverse SDE of a diffusion process can be expressed as dX_t = [f(X_t,t) - g(t)²∇log p_t(X_t)]dt + g(t)dW̄_t.67% similarUnverifiedImplicit neural networks here refer to using a small neural network to directly parameterize the warping function φ, with normalized time coordinates as input and the corresponding alignment positions as output.64% similar
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