# Fenchel Tilting: Weighted Correction for Efficient Finetuning of Generative Models

arXiv: https://arxiv.org/abs/2609.40030 · HTML: https://mlsanity.com/paper/2609.40030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 31 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [DreamSim: Learning New Dimensions of Human Visual Similarity using Synthetic Data](https://mlsanity.com/paper/2306.09344/) (2023)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [OptiDICE: Offline Policy Optimization via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2106.10783/) (2021)
- [Energy-Weighted Flow Matching for Offline Reinforcement Learning](https://mlsanity.com/paper/2503.04975/) (2025)
- [Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2404.19739/) (2024)
- [On the Guidance of Flow Matching](https://mlsanity.com/paper/2502.02150/) (2025)
- [Online Reward-Weighted Fine-Tuning of Flow Matching with Wasserstein Regularization](https://mlsanity.com/paper/2502.06061/) (2025)
- [Fine-tuning of diffusion models via stochastic control: entropy regularization and beyond](https://mlsanity.com/paper/2403.06279/) (2024)
- [Diffusion-DICE: In-Sample Diffusion Guidance for Offline Reinforcement Learning](https://mlsanity.com/paper/2407.20109/) (2024)
- [Tilt Matching for Scalable Sampling and Fine-Tuning](https://mlsanity.com/paper/2512.21829/) (2025)
- [FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation](https://mlsanity.com/paper/2508.12629/) (2025)
- [Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuning](https://mlsanity.com/paper/2511.22640/) (2025)
- [Efficient Tail-Aware Generative Optimization via Flow Model Fine-Tuning](https://mlsanity.com/paper/2602.16796/) (2026)
- [Diffusion Controller: Framework, Algorithms and Parameterization](https://mlsanity.com/paper/2603.06981/) (2026)

## Abstract (arXiv)

Adapting a pretrained generative model to an arbitrary preference expressed as a utility function underlies reward alignment, guided design, and constraint satisfaction, enabling diverse applications. Existing fine-tuning methods trade off generality against computational cost: they either restrict the family class of supported preferences to keep optimization simple or preserve generality at the expense of efficiency. We introduce Fenchel Tilt Flow Control (FTFC), which decouples utility optimization from generative-model fitting. FTFC first optimizes for a target distribution by jointly fitting an effective reward and density-ratio weights on pretrained samples. Method combines the utility's variational structure with Fenchel duality, supporting general f-divergence penalties that determine how rewards are transformed into an distribution-correction weights. These weights are then frozen and used to modify a diffusion or flow model in a single stage of importance-weighted denoising or flow matching, without differentiating through sampling trajectories. We establish exact duality for concave utilities under suitable conditions and show that weighted fitting reproduces the optimal target distribution for a given utility. Across image and molecule generation benchmarks, FTFC improves over baselines on diverse preference functions, while also being up to 20× more efficient. roposed method enables adaptation beyond expected-reward maximization without complex optimization, while preserving robustness for more general class of the utility functions compared to baselines.