6M-Parameter DRLM Solves Sudoku-Extreme 93.9% of the Time Without a Reverse Diffusion Step

The Draft Refinement Language Model (DRLM), which has only 6M parameters, solves 93.9% of Sudoku-Extreme tasks and 44.4% of Countdown-5 tasks. According to the authors, it outperforms both autoregressive and discrete diffusion baselines on Countdown, Sudoku-Extreme and Maze-Hard. The key difference is that DRLM does not use a reverse diffusion step at all. It revises the whole draft and accepts an edit only if the result improves on an internal metric.

The problem: good tokens do not guarantee a good answer

A draft helps a model reason because it lets the model reconsider every decision in light of the rest. In Sudoku, a digit in one cell makes sense only together with the digits in neighboring cells. Discrete diffusion, with its repeated denoising, does not guarantee that kind of consistency. Each individual token update looks plausible, but taken together the updates are not obliged to produce a better answer. The authors build their method around this gap.

How DRLM works

The system has a single denoiser, and it plays two roles. It is trained to reconstruct every token from uniformly corrupted drafts. Training includes both corrupted and untouched tokens, so the model learns to keep what is correct and fix what is wrong at the same time. The denoiser's predictions directly define the edits, so no reverse diffusion step is needed.

The second role is harder: scoring a candidate. The model's confidence in an existing token has two components. The first is support from the context, meaning the prompt and the rest of the draft. The second is the evidence that comes from the mere fact that the token is visible in the input. This second component inflates confidence in what has already been written. Because the corruption process is known, the authors subtract this self-effect and obtain an estimate of how well the rest of the context supports the token.

Cavity energy and the round loop

Per-token scores are aggregated into "cavity energy." It is computed in a single forward pass, and no additional scoring model is needed. A round works like this:

• the denoiser proposes a parallel edit to the draft;
• the finished candidate is read again in its new context;
• the edit is kept only if the candidate's energy is lower than that of the current draft.

As a result, the process has a rollback criterion. A bad edit does not accumulate, as it can with blind iterative denoising.

What the tests showed

• Benchmarks: Countdown, Sudoku-Extreme, Maze-Hard.
• Baselines: autoregressive and discrete diffusion models; DRLM outperforms them.
• Size: 6M parameters.
• Countdown-5: 44.4%.
• Sudoku-Extreme: 93.9%.

The limitations are also clear. All three benchmarks are synthetic tasks with a rigid, verifiable structure, and the model is tiny. The abstract does not show how the method would behave on open-ended text, code or long reasoning chains. It is also unclear how much of the gain would survive scaling to billions of parameters. The abstract does not give baseline numbers, so the size of the margin has to be checked in the paper itself.

What practitioners can take from this

For those building reasoning systems, the "propose, reread, accept or reject" scheme is valuable in itself. It provides a built-in verifier without a second model, so it adds no cost for a separate reward model or an external judge. If global consistency matters for your tasks (planning, constraints, puzzles, structured output), the method is worth testing through reproduction. The first step is to compare it with your autoregressive baseline at an equal compute budget. It is worth watching whether results appear on natural-language and code tasks. For now, this is a convincing proposal for a class of tasks with verifiable answers, not a ready replacement for a general-purpose LLM.