Grab a Coffee: Future-Aware Guidance for Discrete Diffusion with Compiled Objectives
On the map: Diffusion models → Discrete and text diffusion also fits: Diffusion foundations and sampling
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.
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.
Builds on
32 of 48 references.
Closest ancestors · 10
Same direction, newest first
- 2026Constrained Decoding for Diffusion Language Models via Efficient Inference over Finite Automata8 Jul
- 2026VGB for Masked Diffusion Model: Efficient Test-time Scaling for Reward Satisfaction and Sample Editing26 Jun
- 2026DLM-SWAI: Steering Diffusion Language Models Before They Unmask28 May
- 2026DPRM: A Plug-in Doob h transform-induced Token-Ordering Module for Discrete Diffusion Models27 Apr
- 2026Breaking the Factorization Barrier in Diffusion Language Models9 Feb
- 2025Fine-Tuning Masked Diffusion for Provable Self-Correction1 Oct
- 2025Dream 7B: Diffusion Large Language Models21 Aug
- 2025Constrained Discrete Diffusion12 Mar
- 2025Large Language Diffusion Models14 Feb
- 2024Discrete Copula Diffusion2 Oct
Other references · 22
- 2016Pointer Sentinel Mixture Modelscited by 3,096
- 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
- 2020RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Modelscited by 1,255
- 2018Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Reviewcited by 482
- 2021FUDGE: Controlled Text Generation With Future Discriminatorscited by 376
- 2023Protein Design with Guided Discrete Diffusioncited by 157
- 2024Simple Guidance Mechanisms for Discrete Diffusion Modelscited by 155
- 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 136
- 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 129
- 2022Semantic Probabilistic Layers for Neuro-Symbolic Learningcited by 103
- 2023Tractable Control for Autoregressive Language Generationcited by 65
- 2019On Tractable Computation of Expected Predictionscited by 19
10 more
- 2025DINGO: Constrained Inference for Diffusion LLMscited by 16
- 2025Scaling Probabilistic Circuits via Monarch Matricescited by 9
- 2025TRACE Back from the Future: A Probabilistic Reasoning Approach to Controllable Language Generationcited by 8
- 2024Restructuring Tractable Probabilistic Circuitscited by 7
- 2026Reward-Guided Discrete Diffusion via Clean-Sample Markov Chain for Molecule and Biological Sequence Designcited by 6
- 2026D3LM: A Discrete DNA Diffusion Language Model for Bidirectional DNA Understanding and Generationcited by 6
- 2026Inference-Time Alignment of Diffusion Models via Trust-Region Iterative Twisted Sequential Monte Carlocited by 6
- 2026Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusioncited by 5
- 2026Plug-and-Play Guidance for Discrete Diffusion Models via Gradient-Informed Logit Correctioncited by 3
- 2026The Safety-Aware Denoiser for Text Diffusion Modelscited by 2
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