JANUS: Structured Bidirectional Generation for Guaranteed Constraints and Analytical Uncertainty

Constrained generative modeling is fundamental to applications such as robotic control and autonomous driving, where models must respect physical laws and safety-critical constraints. In real-world settings, these constraints rarely take the form of simple linear inequalities, but instead complex feasible regions that resemble road maps or other structured spatial domains. We propose a constrained generation framework that generates samples directly within such feasible regions while preserving realism. Our method fine-tunes a pretrained generative model to enforce constraints while maintaining generative fidelity. Experimentally, our method exhibits characteristics distinct from existing fine-tuning and training-free constrained baselines, revealing a new compromise between constraint satisfaction and sampling quality.

Synthetic data generation is dominated by the fit-then-sample paradigm: a generative model is trained on a private dataset and then sampled from. Despite its widespread adoption, this paradigm faces three challenges: (1) a new training run is required for every dataset; (2) different data modalities, such as single tables, time series, and relational databases, require task-specific models and feature engineering; and (3) the resulting model is opaque, making its behavior under data constraints difficult to inspect. We propose GENSCRIPT, an inference-only pipeline that eliminates model training. GENSCRIPT computes a deterministic statistical profile of the source data (column types, ranges, missingness, categories, correlations, etc.) and passes it--rather than raw rows--to a language model to infer field semantics and cross-column integrity constraints. A coding agent then compiles the profile and constraints into an executable, auditable sampler. This unified approach supports single-table, temporal, and relational data without task-specific modeling. Across four single-table benchmarks, GENSCRIPT builds generators in 2 minutes and samples 50k rows within 6 seconds, while remaining within a few points of leading methods in marginal fidelity. Notably, it is the only method that perfectly preserves a 1-to-1 mapping between columns in the Adult dataset. On a smart-building dataset, it produces conditional time series that more closely match the real distribution than two baselines and perfectly preserves primary- and foreign-key relationships in the corresponding relational database.

Deep generative models provide state-of-the-art performance across a wide array of applications, with recent studies showing increasing applicability for science and engineering. Despite a growing corpus of literature focused on the integration of physics-based constraints into the generation process, existing approaches fail to enforce strict constraint satisfaction while maintaining sample quality. In particular, training-free constrained sampling methods, while providing per-sample feasibility guarantees, introduce a fundamental mismatch between the training objective and the constrained sampling procedure, often leading to performance degradation. Identifying this training-sampling misalignment as a central limitation of current constrained generative modeling approaches, this paper proposes Constraint-Aware Flow Matching, a novel end-to-end framework that explicitly incorporates constraint projections into the training objective. By aligning the model's learned dynamics with the constrained sampling process, the proposed method mitigates distributional shift induced by projection-based corrections, enabling high-quality constrained generation. The proposed approach is evaluated on three challenging real-world benchmarks, illustrating the generality and efficacy of the method.