# Grab a Coffee: Future-Aware Guidance for Discrete Diffusion with Compiled Objectives

arXiv: https://arxiv.org/abs/2609.35924 · HTML: https://mlsanity.com/paper/2609.35924/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 30 of 32)

- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Tractable Control for Autoregressive Language Generation](https://mlsanity.com/paper/2304.07438/) (2023)
- [Discrete Copula Diffusion](https://mlsanity.com/paper/2410.01949/) (2024)
- [Fine-Tuning Masked Diffusion for Provable Self-Correction](https://mlsanity.com/paper/2510.01384/) (2025)
- [On Tractable Computation of Expected Predictions](https://mlsanity.com/paper/1910.02182/) (2019)
- [Constrained Discrete Diffusion](https://mlsanity.com/paper/2503.09790/) (2025)
- [DINGO: Constrained Inference for Diffusion LLMs](https://mlsanity.com/paper/2505.23061/) (2025)
- [Breaking the Factorization Barrier in Diffusion Language Models](https://mlsanity.com/paper/2603.00045/) (2026)
- [Scaling Probabilistic Circuits via Monarch Matrices](https://mlsanity.com/paper/2506.12383/) (2025)
- [TRACE Back from the Future: A Probabilistic Reasoning Approach to Controllable Language Generation](https://mlsanity.com/paper/2504.18535/) (2025)
- [Restructuring Tractable Probabilistic Circuits](https://mlsanity.com/paper/2411.12256/) (2024)
- [Reward-Guided Discrete Diffusion via Clean-Sample Markov Chain for Molecule and Biological Sequence Design](https://mlsanity.com/paper/2602.09424/) (2026)
- [D3LM: A Discrete DNA Diffusion Language Model for Bidirectional DNA Understanding and Generation](https://mlsanity.com/paper/2603.01780/) (2026)
- [Inference-Time Alignment of Diffusion Models via Trust-Region Iterative Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2605.25123/) (2026)
- [Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusion](https://mlsanity.com/paper/2605.23346/) (2026)
- [Constrained Decoding for Diffusion Language Models via Efficient Inference over Finite Automata](https://mlsanity.com/paper/2607.07026/) (2026)
- [DPRM: A Plug-in Doob h transform-induced Token-Ordering Module for Discrete Diffusion Models](https://mlsanity.com/paper/2604.24357/) (2026)
- [Plug-and-Play Guidance for Discrete Diffusion Models via Gradient-Informed Logit Correction](https://mlsanity.com/paper/2606.06303/) (2026)
- [The Safety-Aware Denoiser for Text Diffusion Models](https://mlsanity.com/paper/2605.08116/) (2026)

## Abstract (arXiv)

Discrete diffusion models generate sequences by iteratively resolving multiple tokens in parallel, offering a flexible alternative to left-to-right generation. However, guiding this process with a sequence-level objective is difficult because the value of one unresolved token depends on the other tokens with which it can form a high-reward sequence. Enumerating all such completions makes the whole guidance computation grow exponentially with the number of unresolved positions. We introduce COFFEE, a plug-and-play framework that avoids this enumeration by separating sequence dependence from the objective. At each diffusion step, a target-free carrier absorbs the marginal token distributions predicted by the denoiser to construct a joint model over the unresolved tokens, while a compiled finite-state model records how their combinations affect the sequence-level preference. Pairing their states allows COFFEE to transfer global preferences to unresolved positions and sample a clean reconstruction without retraining the diffusion model. The same framework supports explicit hard constraints and learned soft objectives. We evaluate COFFEE across multiple symbolic, language, and biological benchmarks, where it achieves strong control results with task-dependent quality and diversity trade-offs. By making objectives available to inference rather than only evaluation, COFFEE brings joint conditioning, completion-weighted guidance, and optimization-based constraints into pretrained neural generation, showing the potential of neural-symbolic methods in diffusion guidance.