To circumvent this issue, we investigate the parameter-efficient adaptation of binary-quantized generative models for image editing, and leverage their inherent characteristic that the exact intermediate quantized representations of a source im-Changeage are attainable,birenablingd Xmore effective supervision for precise image inversion.

A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift along the support of the data distribution but not away from it. In this work, we investigate this phenomenon of robustness of the support by taking a dynamical systems approach on the generating stochastic/deterministic process. Our perturbation analysis of the probability flow reveals that infinitesimal learning errors cause the predicted density to be different from the target density only on the data manifold for a wide class of generative models. Further, what is the dynamical mechanism that leads to the robustness of the support? We show that the alignment of the top Lyapunov vectors (most sensitive infinitesimal perturbation directions) with the tangent spaces along the boundary of the data manifold leads to robustness and prove a sufficient condition on the dynamics of the generating process to achieve this alignment. Moreover, the alignment condition is efficient to compute and, in practice, for robust generative models, automatically leads to accurate estimates of the tangent bundle of the data manifold. Using a finite-time linear perturbation analysis on samples paths as well as probability flows, our work complements and extends existing works on obtaining theoretical guarantees for generative models from a stochastic analysis, statistical learning and uncertainty quantification points of view. Our results apply across different dynamical generative models, such as conditional flow-matching and score-based generative models, and for different target distributions that may or may not satisfy the manifold hypothesis.

Protein fitness optimization involves finding a protein sequence that maximizes desired quantitative properties in a combinatorially large design space of possible sequences. Recent advances in steering protein generative models (e.g., diffusion models and language models) with labeled data offer a promising approach. However, most previous studies have optimized surrogate rewards and/or utilized large amounts of labeled data for steering, making it unclear how well existing methods perform and compare to each other in real-world optimization campaigns where fitness is measured through low-throughput wet-lab assays. In this study, we explore fitness optimization using small amounts (hundreds) of labeled sequencefitness pairs and comprehensively evaluate strategies such as classifier guidance and posterior sampling for guiding generation from different discrete diffusion models of protein sequences. We also demonstrate how guidance can be integrated into adaptive sequence selection akin to Thompson sampling in Bayesian optimization, showing that plug-and-play guidance strategies offer advantages over alternatives such as reinforcement learning with protein language models. Overall, we provide practical insights into how to effectively steer modern generative models for next-generation protein fitness optimization.

We address this need by presenting a novel approach based on conformal prediction techniques to create a'confidence mask' capable of reliably and intuitively communicating where the generated image can be trusted. Our method is adaptable to any black-box generative model, including those locked behind an opaque API, requires only easily attainable data for calibration, and is highly customizable via the choice of a local image similarity metric. We prove strong theoretical guarantees for our method that span fidelity error control (according to our local image similarity metric), reconstruction quality, and robustness in the face of data leakage. Finally, we empirically evaluate these results and establish our method's solid performance.

Recent advances in Structure-based Drug Design (SBDD) have leveraged generative models for 3D molecular generation, predominantly evaluating model performance by binding affinity to target proteins. However, practical drug discovery necessitates high binding affinity along with synthetic feasibility and selectivity, critical properties that were largely neglected in previous evaluations. To address this gap, we identify fundamental limitations of conventional diffusion-based generative models in effectively guiding molecule generation toward these diverse pharmacological properties. We propose CBYG, a novel framework extending Bayesian Flow Network into a gradient-based conditional generative model that robustly integrates property-specific guidance. Additionally, we introduce a comprehensive evaluation scheme incorporating practical benchmarks for binding affinity, synthetic feasibility, and selectivity, overcoming the limitations of conventional evaluation methods. Extensive experiments demonstrate that our proposed CBYG framework significantly outperforms baseline models across multiple essential evaluation criteria, highlighting its effectiveness and practicality for real-world drug discovery applications.

Medical Lay Language Generation (MLLG) plays a vital role in improving the accessibility of complex scientific content for broader audiences. Recent literature to MLLG commonly employ parameter-efficient fine-tuning methods such as LowRank Adaptation (LoRA) to fine-tuning large language models (LLMs) using paired expert-lay language datasets. However, LoRA struggles with the challenges posed by multi-source heterogeneous MLLG datasets. Specifically, through a series of exploratory experiments, we reveal that standard LoRA fail to meet the requirement for semantic fidelity and diverse lay-style generation in MLLG task. To address these limitations, we propose Magical, an asymmetric LoRA architecture tailored for MLLG under heterogeneous data scenarios. Magical employs a shared matrix Afor abstractive summarization, along with multiple isolated matrices B for diverse lay-style generation. To preserve semantic fidelity during the lay language generation process, Magical introduces a Semantic Invariance Constraint to mitigate semantic subspace shifts on matrix A. Furthermore, to better adapt to diverse lay-style generation, Magical incorporates the Recommendation-guided Switch, an externally interface to prompt the LLM to switch between different matrices B. Experimental results on three real-world lay language generation datasets demonstrate that Magical consistently outperforms prompt-based methods, vanilla LoRA, and its recent variants, while also reducing trainable parameters by 31.66%.

Designing algorithms for solving high-dimensional Bayesian inverse problems directly in infinite-dimensional function spaces--where such problems are naturally formulated--is crucial to ensure stability and convergence as the discretization of the underlying problem is refined. In this paper, we contribute to this line of work by analyzing a widely used sampler for linear inverse problems: Langevin dynamics driven by score-based generative models (SGMs) acting as priors, formulated directly in function space. Building on the theoretical framework for SGMs in Hilbert spaces, we give a rigorous definition of this sampler in the infinite-dimensional setting and derive, for the first time, error estimates that explicitly depend on the approximation error of the score. As a consequence, we obtain sufficient conditions for global convergence in Kullback-Leibler divergence on the underlying function space. Preventing numerical instabilities requires preconditioning of the Langevin algorithm and we prove the existence and the form of an optimal preconditioner. The preconditioner depends on both the score error and the forward operator and guarantees a uniform convergence rate across all posterior modes. Our analysis applies to both Gaussian and a general class of non-Gaussian priors. Finally, we present examples that illustrate and validate our theoretical findings.

We investigate language generation in the limit - a model by Kleinberg and Mullainathan [2024, NeurIPS] and extended by Li, Raman, and Tewari [2025]. While Kleinberg and Mullainathan proved generation is possible for all countable collections, [Li et al., 2025] defined a hierarchy of generation notions (uniform, non-uniform, and generatable) and explored their feasibility for uncountable collections. Our first set of results resolve two open questions of [Li et al., 2025] by proving finite unions of generatable or non-uniformly generatable classes need not be generatable. These follow from a stronger result: there is a non-uniformly generatable class and a uniformly generatable class whose union is non-generatable. This adds to the aspects along which language generation in the limit is different from traditional tasks in statistical learning theory like classification, which are closed under finite unions. In particular, it implies that given two generators for different collections, one cannot combine them to obtain a single "more powerful" generator, prohibiting this notion of boosting. Our construction also addresses a third of [Li et al., 2025]'s open questions on whether there are uncountable classes that are non-uniformly generatable and do not satisfy the eventually unbounded closure (EUC) condition introduced by Li, Raman, and Tewari. Our approach utilizes carefully constructed classes along with a novel diagonalization argument that could be of independent interest in the growing area of language generation.

Generative modeling is increasingly important for data-driven computational design. Conventional approaches pair a generative model with a discriminative model to select or guide samples toward optimized designs. Yet discriminative models often struggle in data-scarce settings, common in scientific applications, and are unreliable in the tails of the distribution where optimal designs typically lie. We introduce generative property enhancer (GPE), an approach that implicitly guides generation by matching samples with lower property values to higher-value ones. Formulated as conditional density estimation, our framework defines a target distribution with improved properties, compelling the generative model to produce enhanced, diverse designs without auxiliary predictors. GPE is simple, scalable, end-to-end, modality-agnostic, and integrates seamlessly with diverse generative model architectures and losses. We demonstrate competitive empirical results on standard in silico offline (non-sequential) protein fitness optimization benchmarks. Finally, we propose iterative training on a combination of limited real data and self-generated synthetic data, enabling extrapolation beyond the original property ranges.

The widespread use of generative models has created a feedback loop, in which each version of a model is trained on data partially produced by its predecessors. This process has raised concerns about model collapse: A critical degradation in performance caused by repeated training on synthetic data. However, different analyses in the literature have reached different conclusions as to the severity of model collapse. As such, it remains unclear how concerning this phenomenon is, and under which assumptions it can be avoided. To address this, we theoretically study model collapse for maximum likelihood estimation (MLE), in a natural setting where synthetic data is gradually added to the original data set. Under standard assumptions (similar to those long used for proving asymptotic consistency and normality of MLE), we establish non-asymptotic bounds showing that collapse can be avoided even as the fraction of real data vanishes. On the other hand, we prove that some assumptions (beyond MLE consistency) are indeed necessary: Without them, model collapse can occur arbitrarily quickly, even when the original data is still present in the training set. To the best of our knowledge, these are the first rigorous examples of iterative generative modeling with accumulating data that rapidly leads to model collapse.