A new preprint reports that two nested sampling methods were able to steer a discrete diffusion language model toward a chosen sequence-level reward while it generated text, without retraining the model. In the paper’s central comparison, NSMC and FA-NSMC recorded the highest reported toxicity rates and lower perplexity than the base model, best-of-n and bootstrap SMC.
That finding needs a careful reading. Toxicity was the reward used to test controllability, so a higher toxicity rate meant stronger movement toward the selected toxic-class signal in this experiment—not safer output. Perplexity was used as a proxy for fluency, and the paper’s outcomes were automated model scores.
The change happens during generation
These are inference-time methods: they change the sampling process as text is produced instead of retraining the model. NSMC stands for nested sequential Monte Carlo, while FA-NSMC is the paper’s variant. The comparisons included the base MDLM, best-of-n and bootstrap SMC. Later tests varied three settings: outer particles, inner proposals and reconstructions.
The paper also revisits the weighting behind an earlier nested-SMC scheme. It says that scheme was not properly weighted and introduced systematic bias, then develops correctly weighted NSMC variants for discrete diffusion steering.
For toxicity, the reward was the toxic-class log-softmax score from an off-the-shelf RoBERTa classifier, with the steering strength fixed at λ = 10; a holdout toxicity classifier was also used. The perplexity reward came from GPT-2-XL applied to intermediate x0 reconstructions—partial versions of the text as generation proceeded.
The evaluation used the publicly released MDLM checkpoint. For each configuration, the study generated 10 independent 100-token continuations from each of 15 prompts, or 150 generations, with default sampling over 50 diffusion steps.
The main comparison
At N = 4 outer particles, the reported toxicity/perplexity pairs were 0.003/85.3 for Base MDLM, 0.022/55.5 for best-of-n, 0.25/49.0 for bootstrap SMC, 0.39/42.3 for NSMC and 0.40/42.9 for FA-NSMC.
The table displayed point estimates without uncertainty intervals or replicate-level variation. That leaves the size and stability of the gaps unquantified.
Where the settings mattered
Changing the reward-window length produced a clear pattern in one sweep. With N = 8, M = 8 and K = 4, moving from a 50-token window to a 300-token window was accompanied by toxicity rates falling from 0.57 to 0.29 for SMC, 0.70 to 0.30 for NSMC and 0.68 to 0.47 for FA-NSMC. At the longest window, FA-NSMC remained highest.
More inner proposals did not keep adding the same gains. At N = 8 and K = 4, NSMC toxicity values were 0.57, 0.71 and 0.70 as M rose from 1 to 8 to 32; FA-NSMC values were 0.54, 0.68 and 0.71. The authors describe these gains as largely plateauing.
The paper’s broader scaling discussion identifies outer-particle count as the dominant compute-allocation factor, reconstruction count as a source of stronger guidance and inner proposals as a setting with diminishing returns. In 10 repeated runs from the N = 8 block, SMC was 0.57 at K = 4 and 0.67 at K = 16; at M = 8, NSMC was 0.70 and 0.74, while FA-NSMC was 0.68 and 0.74 at those two K settings. Dispersion estimates were not reported.
A warning from the weighting test
An internal diagnostic pointed to the importance of the weighting correction. Correctly weighted potentials—intermediate reward calculations—showed increasing expected rewards for NSMC and FA-NSMC. A biased version that omitted a denominator did not show that increase and was reported not to target the correct distribution.
On the paper’s diversity measures, best-of-n had the highest displayed values in the toxicity setting. At N = 8, K = 4 and λ = 10, its Distinct-1/Distinct-2 scores were 0.29/0.74, compared with 0.26/0.71 for SMC, 0.26/0.70 for NSMC and 0.26/0.71 for FA-NSMC.
A narrow test, not a safety verdict
The evidence remains narrow. The evaluation covered only toxicity and perplexity on a single base checkpoint, and the authors warn that approximate x0 reconstructions and off-the-shelf reward models may be noisy and high-variance.
Those limits mean the preprint is evidence about controllability under the tested automated scores, not about reduced real-world toxicity or human-judged fluency. Whether the methods transfer to other discrete diffusion models, domains or broader safety and controllable-generation benchmarks remains open.
The front matter says the work was accepted as a workshop paper at ReALM-GEN, ICLR 2026; it remains a preprint.
Paper data and sources
Original title: Discrete Diffusion Inference-Time Control with Nested Sequential Monte Carlo
Authors: Lohithsai Yadala Chanchu, Hany Abdulsamad, Christian A. Naesseth
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text