Discrete diffusion models generate sequences by resolving multiple tokens in parallel, avoiding the constraints of left‑to‑right generation. Guiding this process with a sequence‑level objective is hard because the value of an unresolved token depends on the other tokens it may combine with to form a high‑reward sequence. Enumerating all completions makes the computation grow exponentially with the number of unresolved positions. COFFEE avoids enumeration by separating sequence dependence from the objective. At each diffusion step a target‑free carrier absorbs the marginal token distributions from the denoiser to build a joint model over the unresolved tokens, while a compiled finite‑state model records how their combinations affect the sequence preference. Pairing the two states lets COFFEE transfer global preferences to unresolved positions and sample a clean reconstruction without retraining the diffusion model. The framework also supports explicit hard constraints and learned soft objectives. Experiments on symbolic, language and biological benchmarks show that COFFEE achieves strong control with task‑dependent trade‑offs between quality and diversity. By making objectives available during inference rather than only for evaluation, COFFEE brings joint conditioning, completion‑weighted guidance and optimization‑based constraints into pretrained neural generation, highlighting the promise of neural‑symbolic methods in diffusion guidance.
Review