It is proved that any corrector measurable with respect to past observations leaves at least the conditional variance of the statistic it tracks, and that trend extrapolation beats trusting the last observation only when $\mu^2>v(1-2\rho)$.
Abstract
Generative models of temporal graphs are trained on one stretch of an evolving network and deployed on the next, and they degrade badly in the gap. We show this degradation is derivable, general, and not fixable from observations. The masked flow-matching loss decomposes exactly, with no independence assumption, into an irreducible entropy plus a divergence whose derivative along the training path is positive precisely for structures rare during training and common at deployment, diverging as their training probability goes to zero. Empirically the trade-off is a power law with exponent $-0.605$ ($R^2=0.9977$), and drift raises the sampler's error floor without changing how many steps reach it: across seven well-powered conditions the drift-period marginal error varies by at most $6\%$ over a $50\times$ range of sampling budgets, while the floor sits $2.2\times$ to $34.3\times$ above the in-period floor. Because the deployment period is observed, correction looks like a matter of measurement. It is not. We prove that any corrector measurable with respect to past observations leaves at least the conditional variance of the statistic it tracks, and that trend extrapolation beats trusting the last observation only when $\mu^2>v(1-2\rho)$. Both premises are measurable and both go the wrong way: the drift is trendless and mean-reverting, with a one-step innovation as large as the drift itself. An oracle removes $60\%$ of the error, the best observation-based corrector recovers $5.7\%$ of that, and extrapolation is strictly worse than doing nothing clever.
Denoising Diffusion Probabilistic Models (DDPMs) generate samples by starting from noise and repeatedly denoising while keeping each update close to the current noisy state. This behavior is effective in many continuous domains, but its role is less clear for globally constrained discrete tasks, such as Sudoku, graph connectivity, Latin squares, and N-queens. In such settings, early discrete errors can be difficult to undo. As a result, standard diffusion sampling may preserve early mistakes, even when the model's clean predictions are informative. We compare standard samplers to sampling directly from the model's clean prediction. Without retraining, this single change improves Sudoku validity from 31% to 95%, with consistent gains across the other discrete tasks. We hypothesize that staying close to the current noisy state is harmful because the reverse trajectory can drift off the forward noising distribution the model was trained on. To reduce this train-test mismatch, we further introduce self-correction training, which exposes the model to its own predictions, improving robustness to errors that arise during inference. This substantially improves the performance of standard samplers. Our results suggest that continuous diffusion models can learn nontrivial global constraints, but discrete reasoning tasks require better alignment between training and inference: either through samplers that reduce commitment to early decisions, or through training that teaches the model to correct its own inference-time errors.
M. Drozdova, Stéphane Liem Nguyen, François Fleuret· 0 citations
Discrete diffusion, including remasking and uniform-state samplers, generate a sequence by writing multiple token positions per step, drawing each from a per-position distribution and choosing which positions to write from those same distributions. For domains of general interest (pixels, phonemes, or words) there are inherent dependencies between tokens. We show that a step matches the training distribution only when the positions it writes are conditionally independent given the tokens already fixed, that no product of per-position distributions can match a dependent group, and that per-position distributions do not determine whether a group is dependent: two joint distributions can have identical per-position marginals while differing in which combinations of values occur. On ScanAndAdd, a synthetic task whose joint distribution is available in closed form, we verify that every group of two or more undetermined positions a confidence ranking writes is dependent, and measure the generated distribution to be $29\times$ the sampling-noise floor total variation while per-sample metrics are $1.0$.
Russ Webb, Amitis Shidani, Alice Bizeul et al.· 0 citations
Simplax is introduced, an exact Dirichlet--categorical augmentation that couples each corrupted categorical state with an auxiliary simplex-valued variable while preserving the original uniform diffusion process as its categorical marginal.
Jinya Sakurai, Patrick Pynadath, Satoshi Hayakawa et al.· 1 citation
Game Theoretic Anticipatory Continual Graph Learning (GT-ACGL), a framework that casts fraud detection as a continuous Stackelberg game between a defender and an adaptive adversary, and encourages decision boundaries that remain comparatively stable under strategic structural perturbation.
Hui-Jie Fan, Ya-Nan Jiao, M. Wang et al.· Scientific Reports· 2 citations
This work derives a bias-variance decomposition of the expected gap between the model's and target's collision probabilities, showing that SFT is not inherently biased toward mode collapse or its opposite, and shows that diversity miscalibration can arise from finite-sample error and shrink as SFT better approximates the target distribution.
A 170M-parameter M2S model trained on about 262B OpenWebText token slots outperforms the evaluated pure-uniform SEDD, GIDD, and Neural CTMC checkpoints at every tested sampling budget, reaching generative PPL $143.3$ at 128 steps versus $183.6$ for the strongest pure-uniform baseline.
