arXiv:2610. 10190v1 Announce Type: cross Abstract: We analyze the first-order deterministic diffusion sampler of Karras et al.
arXiv:2606. 13796v1 Announce Type: cross Abstract: Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution.
arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.
arXiv:2607. 26285v1 Announce Type: cross Abstract: Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees.
The paper introduces an information-theoretic measure called model information to quantify how much a diffusion model’s outputs depend on its specific training dataset. By analyzing how this measure scales with model size and dataset size, the authors identify two distinct regimes: a nonlinear regime where memorization transitions to imperfect generalization, and a linear regime where generalization improves and sample quality rises. They propose a scaling law that captures these regimes and demonstrate that it can predict memorization and sample quality beyond the fitted data range.
arXiv:2610.34834v1 Announce Type: new Abstract: Clean-image prediction ($x$-prediction) and noise prediction yield equivalent population-optimal denoisers, yet can perform very differently in finite...
arXiv:2610.07655v1 Announce Type: cross Abstract: Discrete diffusion models have emerged as a practically successful framework for generative modeling on discrete product spaces, yet their statistica...
The paper establishes finite‑sample guarantees for fully discrete conditional diffusion models trained from data and run with a finite number of denoising steps. By aligning the score‑training objective with the sampling grid, the authors jointly analyze statistical estimation and numerical discretization errors. For any smoothness index β>0, they prove that an appropriately chosen grid yields an averaged conditional Kullback–Leibler divergence of ˗O_p(n^{-2β/(d_x+d_y+2β)}) and a total‑variation error of ˗O_p(n^{-β/(d_x+d_y+2β)}), matching known rates up to logarithmic factors.
arXiv:2607. 08757v1 Announce Type: cross Abstract: Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory.
arXiv:2610. 12052v1 Announce Type: cross Abstract: Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear.
arXiv:2605.08392v2 Announce Type: replace Abstract: Practical diffusion sampling requires simulating a reverse-time ODE or SDE with a limited number of denoising steps, making the choice of sampling...
arXiv:2610. 02663v1 Announce Type: cross Abstract: Despite the remarkable empirical success of flow-matching models, their statistical generalization guarantees remain underdeveloped.
arXiv:2602. 02908v2 Announce Type: replace-cross Abstract: Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed.