# Error-Corrected Inference-Time Scaling for Imperfect Diffusion Models

arXiv: https://arxiv.org/abs/2610.01933 · HTML: https://mlsanity.com/paper/2610.01933/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 41 of its 53 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 41)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Hutch++: Optimal Stochastic Trace Estimation](https://mlsanity.com/paper/2010.09649/) (2020)
- [Gradient Guidance for Diffusion Models: An Optimization Perspective](https://mlsanity.com/paper/2404.14743/) (2024)
- [Learning Interpolations between Boltzmann Densities](https://mlsanity.com/paper/2301.07388/) (2023)
- [Scalable Equilibrium Sampling with Sequential Boltzmann Generators](https://mlsanity.com/paper/2502.18462/) (2025)
- [Blindness of score-based methods to isolated components and mixing proportions](https://mlsanity.com/paper/2008.10087/) (2020)
- [Accurate transition state generation with an object-aware equivariant elementary reaction diffusion model](https://mlsanity.com/paper/2304.06174/) (2023)
- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo](https://mlsanity.com/paper/2502.12786/) (2025)
- [Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence](https://mlsanity.com/paper/2412.18164/) (2024)
- [Learning normalized image densities via dual score matching](https://mlsanity.com/paper/2506.05310/) (2025)
- [RNE: plug-and-play diffusion inference-time control and energy-based training](https://mlsanity.com/paper/2506.05668/) (2025)
- [Test-time scaling of diffusions with flow maps](https://mlsanity.com/paper/2511.22688/) (2025)
- [Density Ratio Estimation with Conditional Probability Paths](https://mlsanity.com/paper/2502.02300/) (2025)

## Abstract (arXiv)

Inference-time scaling adapts pretrained diffusion models to new sampling tasks without additional training. Existing methods rely primarily on Monte Carlo sampling with more particles, yet are premised on the pretrained model being exact. In practice, data and training limitations make the model imperfect, and these methods inherit its error. More particles reduce Monte Carlo error but cannot remove the mismatch between the endpoint and the desired target or the error in tracking the prescribed probability path. We introduce the Energy-based Feynman-Kac Corrector (EBFKC), a framework for energy-based diffusion models that corrects these errors on the fly given a reference energy. We first derive Feynman-Kac dynamics that track a prescribed path exactly in the continuous-time population limit even when the model is imperfect, and approximate these dynamics using sequential Monte Carlo with variance-controlling guidance. To remove the endpoint mismatch, we use the pretrained energy as a surrogate along the diffusion path and progressively incorporate the discrepancy between the learned and target terminal energies. Experiments on Gaussian mixture models, particle systems, alanine dipeptide, and alanine tetrapeptide show that our method closely matches target distributions and molecular free-energy profiles under annealing and reward tilting, whereas standard inference-time scaling baselines retain substantial sampling errors.