{"ID":2841147,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.11956","arxiv_id":"2511.11956","title":"On the Time Derivative of the KL Divergence for a Generalized Langevin Annealing Scheme","abstract":"Consider the Langevin diffusion process $\\mathrm{d} X_t = \\nabla \\log p_t(X_t) + \\sqrt{2}\\mathrm{d} W_t$ guided by the time-dependent probability density $p_t(x)$. Let $q_t$ be the density of $X_t$. Recently, in order to analyze convergence in the Kullback-Leibler divergence, the time derivative of $t\\mapsto \\mathrm{KL}(q_t|p_t)$ has been used in several works without investigating in detail when such a derivative exists. In this short manuscript we provide a rigorous derivation of the quantity $\\frac{\\mathrm{d}}{\\mathrm{d} t}\\mathrm{KL}(q_t|p_t)$.","short_abstract":"Consider the Langevin diffusion process $\\mathrm{d} X_t = \\nabla \\log p_t(X_t) + \\sqrt{2}\\mathrm{d} W_t$ guided by the time-dependent probability density $p_t(x)$. Let $q_t$ be the density of $X_t$. Recently, in order to analyze convergence in the Kullback-Leibler divergence, the time derivative of $t\\mapsto \\mathrm{KL...","url_abs":"https://arxiv.org/abs/2511.11956","url_pdf":"https://arxiv.org/pdf/2511.11956v2","authors":"[\"Andreas Habring\"]","published":"2025-11-15T00:09:04Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.PR\"]","methods":"[\"Diffusion Model\"]","has_code":false}