arXiv:2606. 07835v1 Announce Type: new Abstract: A fundamental tension exists in the large-step inference of diffusion models via their deterministic probability flow ordinary differential equation (PF-ODE) trajectories, which we identify as the contractivity trap: efficient inference favors large step sizes, while aggressive steps and highly expressive denoisers can undermine contraction-based stability certificates for error suppression.
By Shigui Li, Delu Zeng
arXiv:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
By Jiadong Liang, Zhihan Huang, Yuxin Chen
arXiv:2606. 14334v1 Announce Type: new Abstract: High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension.
By Jacob Bamberger, Adam Gosztolai, Pierre Vandergheynst, Michael Bronstein, Iolo Jones
arXiv:2606. 13240v1 Announce Type: cross Abstract: A key strength of diffusion models lies in their flexibility, since their outputs can be controlled at sampling time through guidance.
By Rapha\"el Razafindralambo, R\'emy Sun, Fr\'ed\'eric Precioso, Jes Frellsen, Pierre-Alexandre Mattei
arXiv:2606. 02232v1 Announce Type: new Abstract: Learning a Markov transition model is not merely conditional density estimation: the learned object must be a valid transition kernel before it is iterated in downstream dynamics.
By Ao Xu
arXiv:2607. 16685v1 Announce Type: cross Abstract: Conditional diffusion models have become a powerful and flexible framework for learning complex conditional distributions from labeled data.
By Jin Su, Yuan Gao, Yong Zhou, Jian Huang
arXiv:2602. 13362v2 Announce Type: replace-cross Abstract: A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty.
By \'Ad\'am Jung, Domokos M. Kelen, Andr\'as A. Bencz\'ur
Training neural networks to jointly predict mean and uncertainty estimates from noisy observations can be unstable, prompting a series of independent stabilization efforts. We argue that these interventions highlight a common underlying issue where gradient steps are poorly aligned with the geometry of the loss landscape.
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.
By Na\"il B. Khelifa, Richard E. Turner, Ramji Venkataramanan
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.
By Yiwei Zhou
arXiv:2606. 07399v1 Announce Type: cross Abstract: Generative models for counterfactual outcomes have great potential to support decision-making under complex interventions, but existing approaches are limited by unstable estimation, poor generalization across environments, and bias from nuisance model misspecification.
By Raphael C Kim, Jingsen Zhu, Ramin Zabih, Michele Santacatterina
arXiv:2608. 06809v1 Announce Type: new Abstract: How can an analyst decide whether a nonlinear dimensionality reduction embedding can be trusted?
By Xinyu Zhang, Klaus Mueller