# The tractability landscape of diffusion alignment: regularization, rewards, and computational primitives

arXiv: https://arxiv.org/abs/2605.11361 · HTML: https://mlsanity.com/paper/2605.11361/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 13 of its 15 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 13 of 13)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Image Inpainting with Contextual Attention](https://mlsanity.com/paper/1801.07892/) (2018)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [Proteina: Scaling Flow-based Protein Structure Generative Models](https://mlsanity.com/paper/2503.00710/) (2025)
- [What does guidance do? A fine-grained analysis in a simple setting](https://mlsanity.com/paper/2409.13074/) (2024)
- [Diffusion Posterior Sampling is Computationally Intractable](https://mlsanity.com/paper/2402.12727/) (2024)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)
- [ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problems](https://mlsanity.com/paper/2506.10955/) (2025)
- [Posterior Sampling by Combining Diffusion Models with Annealed Langevin Dynamics](https://mlsanity.com/paper/2510.26324/) (2025)
- [Steering diffusion models with quadratic rewards: a fine-grained analysis](https://mlsanity.com/paper/2602.16570/) (2026)
- [Efficient Approximate Posterior Sampling with Annealed Langevin Monte Carlo](https://mlsanity.com/paper/2508.07631/) (2025)

## Built on by (most cited first, 2 of 2)

- [Are we really tilting? The mechanics of reward guidance in flow and diffusion models](https://mlsanity.com/paper/2606.02884/) (2026)
- [Weighted Adjoint Matching: Finetuning Flow Matching Models with Time-Dependent Control Cost](https://mlsanity.com/paper/2610.20035/) (2026)

## Abstract (arXiv)

Inference-time reward alignment asks how to turn a pre-trained diffusion model with base law p into a sampler that favors a reward r while remaining close to p. Since there is no canonical distributional distance for this closeness constraint, different choices lead to different "reward-aligned" laws and, just as importantly, different algorithmic problems. We develop a primitive-based approach to reward alignment: rather than assuming arbitrary reward-aligned laws can be sampled, we ask which simple algorithmic primitives suffice to implement alignment for non-trivial reward classes. If closeness is measured in KL distance, the target law is q(x) propto p(x) exp(λ-1r(x)). For this setting, we show that linear exponential tilts of the form q(x)propto p(x)exp(langle θ, x rangle) -- which according to recent work [MRR26] can be efficiently sampled from -- are a sufficient primitive for aligning to a very broad class of convex low-dimensional rewards. If closeness is measured in Wasserstein distance, the corresponding primitive is a proximal transport oracle: given x, solve mboxargmaxy r(y)- λ c(x,y). This oracle can be efficiently implemented for concave or low-dimensional Lipschitz rewards r(x)=f(Ax). Together, these results illustrate that the choice of distribution distance for alignment affects the computational primitive and the tractable reward class.