# Tilt Matching for Scalable Sampling and Fine-Tuning

arXiv: https://arxiv.org/abs/2512.21829 · HTML: https://mlsanity.com/paper/2512.21829/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 29 of its 57 references that are in the map.
- First posted on arXiv 26 Dec 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024)
- [Proteina: Scaling Flow-based Protein Structure Generative Models](https://mlsanity.com/paper/2503.00710/) (2025)
- [DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transform](https://mlsanity.com/paper/2406.01781/) (2024)
- [Efficient Diversity-Preserving Diffusion Alignment via Gradient-Informed GFlowNets](https://mlsanity.com/paper/2412.07775/) (2024)
- [LEAPS: A discrete neural sampler via locally equivariant networks](https://mlsanity.com/paper/2502.10843/) (2025)
- [Improving GFlowNets for Text-to-Image Diffusion Alignment](https://mlsanity.com/paper/2406.00633/) (2024)
- [Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2506.16471/) (2025)
- [Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference](https://mlsanity.com/paper/2508.12511/) (2025)
- [Transport meets Variational Inference: Controlled Monte Carlo Diffusions](https://mlsanity.com/paper/2307.01050/) (2023)

## Built on by (most cited first, 22 of 22)

- [Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Models](https://mlsanity.com/paper/2605.10759/) (2026)
- [Lookahead Sample Reward Guidance for Test-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2602.03211/) (2026)
- [Diffusion Reinforcement Learning via Centered Reward Distillation](https://mlsanity.com/paper/2603.14128/) (2026)
- [Flow Sampling: Learning to Sample from Unnormalized Densities via Denoising Conditional Processes](https://mlsanity.com/paper/2605.03984/) (2026)
- [Designing Reinforcement Learning for Diffusion Models: A Unified Path-Space View](https://mlsanity.com/paper/2608.14430/) (2026)
- [Discrete Tilt Matching](https://mlsanity.com/paper/2604.18739/) (2026)
- [Diffusion Alignment Beyond KL: Variance Minimisation as Effective Policy Optimiser](https://mlsanity.com/paper/2602.12229/) (2026)
- [The critical slowing down in training diffusion models](https://mlsanity.com/paper/2605.12597/) (2026)
- [The Reward Was in Your Data All Along: Correcting Flow Matching with Discriminator-Guided RL](https://mlsanity.com/paper/2606.19162/) (2026)
- [Minimal-Action Discrete Schr"odinger Bridge Matching for Peptide Sequence Design](https://mlsanity.com/paper/2601.22408/) (2026)
- [Gradual Fine-Tuning for Flow Matching Models](https://mlsanity.com/paper/2601.22495/) (2026)
- [Coarse-Grained Boltzmann Generators](https://mlsanity.com/paper/2602.10637/) (2026)
- [Follow the Mean: Reference-Guided Flow Matching](https://mlsanity.com/paper/2605.10302/) (2026)
- [Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling](https://mlsanity.com/paper/2607.15682/) (2026)
- [Denoising as Projection: Constrained Optimization with Gradient-Guided Diffusion](https://mlsanity.com/paper/2608.29507/) (2026)
- [Interacting particle guidance for sampling reward-tilted generative priors](https://mlsanity.com/paper/2609.37227/) (2026)
- [Fenchel Tilting: Weighted Correction for Efficient Finetuning of Generative Models](https://mlsanity.com/paper/2609.40030/) (2026)
- [Best-of-N Guidance for Test-time Diffusion Alignment](https://mlsanity.com/paper/2610.05108/) (2026)
- [DiffusionART: Efficient, Stable and Scalable Reinforcement of Diffusion Models](https://mlsanity.com/paper/2610.12572/) (2026)
- [Reinforcement Learning via Fixed-point Flow Matching](https://mlsanity.com/paper/2610.12848/) (2026)
- [On the Design Space of Continuous Diffusion Language Models](https://mlsanity.com/paper/2610.13834/) (2026)
- [Weighted Adjoint Matching: Finetuning Flow Matching Models with Time-Dependent Control Cost](https://mlsanity.com/paper/2610.20035/) (2026)

## Abstract (arXiv)

We propose a simple, scalable algorithm for using stochastic interpolants to sample from unnormalized densities and for fine-tuning generative models. The approach, Tilt Matching, arises from a dynamical equation relating the flow matching velocity to one targeting the same distribution tilted by a reward, implicitly solving a stochastic optimal control problem. The new velocity inherits the regularity of stochastic interpolant transports while also being the minimizer of an objective with strictly lower variance than flow matching itself. The update to the velocity field can be interpreted as the sum of all joint cumulants of the stochastic interpolant and copies of the reward, and to first order is their covariance. The algorithms do not require any access to gradients of the reward or backpropagating through trajectories of the flow or diffusion. We empirically verify that the approach is efficient and highly scalable, providing state-of-the-art results on sampling under Lennard-Jones potentials and is competitive on fine-tuning Stable Diffusion, without requiring reward multipliers. It can also be straightforwardly applied to tilting few-step flow map models.