Are we really tilting? The mechanics of reward guidance in flow and diffusion models

Reward guidance algorithms steer a learned generative process toward the reward-tilted measure at inference time. While empirically powerful, these methods are prone to reward hacking: the guided model over-optimizes the reward at the cost of fidelity to the learned distribution. Prior work has attributed this to the complexity of neural reward functions or implicit biases in diffusion training, but its fundamental origins remain poorly understood. We show that reward hacking arises from an approximation made in most practical implementations of reward-guided diffusion -- finite-particle plug-in estimation of the Doob h-function -- even in the simplest non-trivial settings of Gaussian and Gaussian mixture targets with quadratic rewards. In closed form, we isolate two distinct failure modes of the plug-in estimator: it leads to reward hacking within each mode and it cannot select high-reward modes. We propose a closed-form reward damping schedule that corrects the within-mode bias with no additional compute, and clarify the role of best-of-n sampling in compensating for the mode selection failure. Experiments on Gaussian mixture targets, a 2D checkerboard, and FLUX.1 text-to-image generation confirm that our theoretical insights carry over to practical settings.

Downscaling land surface temperature data using edge detection and block-diagonal Gaussian process regression

Accurate and high-resolution estimation of land surface temperature (LST) is crucial in estimating evapotranspiration, a measure of plant water use and a central quantity in agricultural applications. In this work, we develop a novel statistical method for downscaling LST data obtained from NASA's ECOSTRESS mission, using high-resolution data from the Landsat 8 mission as a proxy for modeling agricultural field structure. Using the Landsat data, we identify the boundaries of agricultural fields through edge detection techniques, allowing us to capture the inherent block structure present in the spatial domain. We propose a block-diagonal Gaussian process (BDGP) model that captures the spatial structure of the agricultural fields, leverages independence of LST across fields for computational tractability, and accounts for the change of support present in ECOSTRESS observations. We use the resulting BDGP model to perform Gaussian process regression and obtain high-resolution estimates of LST from ECOSTRESS data, along with uncertainty quantification. Our results demonstrate the practicality of the proposed method in producing reliable high-resolution LST estimates, with potential applications in agriculture, urban planning, and climate studies.

Conformal changepoint localization

Changepoint localization is the problem of estimating the index at which a change occurred in the data generating distribution of an ordered list of data, or declaring that no change occurred. We present the broadly applicable CONCH (CONformal CHangepoint localization) algorithm, which uses a matrix of conformal p-values to produce a confidence interval for a (single) changepoint under the mild assumption that the pre-change and post-change distributions are each exchangeable. We exemplify the CONCH algorithm on a variety of synthetic and real-world datasets, including using black-box pre-trained classifiers to detect changes in sequences of images or text.

Multiple testing in multi-stream sequential change detection

Multi-stream sequential change detection involves simultaneously monitoring many streams of data and trying to detect when their distributions change, if at all. Here, we theoretically study multiple testing issues that arise from detecting changes in many streams. We point out that any algorithm with finite average run length (ARL) must have a trivial worst-case false detection rate (FDR), family-wise error rate (FWER), and per-family error rate (PFER); thus, any attempt to control these Type I error metrics is fundamentally in conflict with the desire for a finite ARL. One of our contributions is to define a new class of metrics which can be controlled, called error over patience (EOP). We propose algorithms that combine the recent e-detector framework (which generalizes the Shiryaev-Roberts and CUSUM methods) with the recent e-Benjamini-Hochberg procedure and e-Bonferroni procedures. We prove that these algorithms control the EOP at any desired level under very general dependence structures on the data within and across the streams. In fact, we prove a more general error control that holds uniformly over all stopping times and provides a smooth trade-off between the conflicting metrics. Additionally, if finiteness of the ARL is forfeited, we show that our algorithms control the Type I error.