ConfHit: Conformal Generative Design with Oracle Free Guarantees

Conformal prediction (CP) and its extension, conformal risk control (CRC), are established frameworks for quantifying uncertainty in supervised machine learning through formal guarantees. However, recent breakthroughs in artificial intelligence (AI) have been driven by unsupervised generative models, such as large language models (LLMs) and image generators, which are not directly compatible with CP or CRC. In this work we introduce conformal generation (Conf-Gen), a general framework adapting CRC to generative tasks while relaxing its theoretical assumptions. Conf-Gen unifies and generalizes previous attempts to apply CP to LLMs, and extends conformal methodology to entirely new domains. We demonstrate the flexibility of Conf-Gen through some novel applications, including obtaining conformal guarantees on: image generators producing non-memorized images, conversational AI systems having asked enough clarifying questions, and the output of AI agents being correct.

Closed-loop generative selection has become a workhorse of computational drug discovery: a learned generative model proposes candidate molecules, a fitness oracle scores them, the best are kept, and the model is retrained on this elite set before the next round. Despite its wide use, the method has lacked a rigorous convergence theory, largely because retraining the model each round breaks the Markov property on which classical evolutionary-algorithm analysis relies. We develop a self-contained theory of convergence and expected running time for this class of algorithms. By recovering a Markov structure on an enlarged state space, we show that elitism makes the search absorbing, and we prove almost-sure convergence together with a runtime bound that decomposes the search into the time spent escaping each fitness level. We then analyse the role of the model's memory---how much of the past it is trained on. When learning improves steadily with more data, deeper memory never hurts; when it does not, an exit-time analysis pinpoints the optimal memory depth and shows that excess memory can actually slow convergence. The theory extends to multi-objective search and to noisy oracles: we quantify how many repeated evaluations certify progress under light-tailed noise, and how robust estimators restore guarantees under heavy tails. Recast in terms of oracle evaluations - the true bottleneck in drug design - the analysis yields a concrete, evaluation-minimal strategy. Areproducible study confirms the predictions, including the surprising cost of excess memory. We close with three open problems.

Generating chemically valid 3D molecular conformations is critical for computational drug discovery. Classical diffusion-based models like GeoLDM perform well but require hundreds of steps, making large-scale in silico screening impractical. Recent efforts on few-step molecular generation have accelerated this process to 12-50 steps, but they often largely sacrifice sample stability. In this work, we present FlashMol, an ultra-fast molecule generative model producing high-quality molecular conformations in as few as 4 steps. To achieve this, we adapt distribution matching distillation (DMD) - a reverse KL-divergence minimization objective - to the molecular domain for effective distillation. Considering the local minimization behavior of DMD, we respace the molecule generation timesteps, providing the generator with much better initialization and enables effective distillation. Additionally, to mitigate the mode-seeking behavior of DMD and improve diversity, we further regularize it with a Jensen-Shannon divergence term, which incorporates the mean-seeking behavior of the forward KL divergence. Extensive experiments on QM9 and GEOM-DRUG datasets demonstrate that FlashMol matches and even surpasses the original 1000-step teacher, achieving up to 250$\times$ acceleration in sampling speed while maintaining high molecular quality.