Noise Your Prompt: Noising Conditioning Tokens in Continuous Diffusion Language Models

Justin Jung

cs.LGOct 6, 2026

Noise Your Prompt: Noising Conditioning Tokens in Continuous Diffusion Language Models

Authors: Justin Jung

Organizations: Lateral Intelligence

Abstract

We revisit a standard accepted practice in the continuous diffusion language model literature of fixing conditioning prompt tokens clean during training. We make a very simple modification: also noise the conditioning prompt tokens during training. We demonstrate that under this modified training objective, we achieve better generalization in combinatorial reasoning tasks such as Sudoku and N-Queens, with the largest gains on harder variants ( $3.73\% \to 24.65\%$ solve rate on Sudoku Hard), and increased diversity of generated solutions ( $50.60\% \to 73.79\%$ coverage on 10x10 N-Queens). We also show measurable improvements to natural language generation quality in modest dataset regimes with Gigaword summarization, but notably demonstrate that gains do not transfer to all natural language tasks (e.g open ended dialogue generation). Our method is a single line change to the training objective, requires no additional inference costs by default, and provides the flexibility of classifier-free guidance inspired guided sampling. Our \href{https://github.com/LateralIntelligence/noise-your-prompt} {code} is publicly available.

Figures & tables

Figure 1: Noising the conditioning tokens improves solution diversity. (a) Five board generations of a single held-out N-Queens ( $8\times 8$ ) puzzle that admits six distinct valid solutions (distinguished by color and letter). A model trained with noised conditioning tokens ( $p_{\text{condclean}}{=}0.2$ , top) spreads its generations across the solution set ( $4/6$ distinct solutions), whereas the standard “paste-in” model that keeps conditioning tokens clean throughout training ( $p_{\text{condclean}}{=}1.0$ , bottom) mode-collapses onto a single completion. (b) Solution coverage as a function of the number of valid solutions admitted by the input board, over $750$ held-out $10\times 10$ puzzles with $k{=}20$ generations each. The noised-prompt model dominates the clean-prompt model at every solution count. We quantify this gap in Section 4.4 .

Panel of Figure 2 — Figure 2: Visualization of our training objective. Standard conditional training keeps conditioning tokens at fixed clean noise level ( $t^{\prime}{=}1$ ). In contrast, we train over a range of conditioning noise levels (blue region), exposing the model to a range of conditioning levels. At generation time we follow standard practice and integrate with the conditioning tokens held clean.

Figure 3: Puzzle solve rate over the sampling trajectory. Puzzle (exact match) solve rate as a function of sampling time (noisy input solution $\rightarrow$ clean solution), read from the model’s $x_{1}$ prediction at each step. Means calculated over $2000$ held-out puzzles with a $128$ -step Euler sampler; shaded bands are single-seed $95\%$ bootstrap intervals over puzzles. Across both difficulties the noised-prompt models ( $p_{\text{condclean}}{=}0.2,0.5$ ) reach a substantially higher solve rate than the standard paste-in model ( $p_{\text{condclean}}{=}1.0$ ) and also saturate their solve rate bound earlier in generation.

	Easy ( $40/81$ clues)		Hard ( $30/81$ clues)
$p_{\text{condclean}}$	$N=10{,}000$	$N=1{,}000$	$N=10{,}000$	$N=1{,}000$
$0.0$ (uncond.)	$1.41$	$0.00$	$0.00$	$0.00$
	$[0.03,\,2.79]$	$[0.00,\,0.00]$	$[0.00,\,0.00]$	$[0.00,\,0.00]$
$0.1$	$88.59$	$2.42$	$\mathbf{24.65}$	$0.02$
	$[85.88,\,91.30]$	$[0.00,\,4.99]$	$[18.56,\,30.74]$	$[0.00,\,0.08]$
$0.2$	$88.89$	$1.39$	$24.25$	$0.01$

Table 1: Sudoku solve rate (%) on

2{,}000

held-out puzzles under the conditioning clean probability

p_{\text{condclean}}

	$n=8$ (length 64)		$n=10$ (length 100)
$p_{\text{condclean}}$	Accuracy	Coverage	Accuracy	Coverage
$0.2$	$\mathbf{99.37}$	$\mathbf{92.39}$	$\mathbf{98.32}$	$\mathbf{73.79}$
	$[99.07,\,99.66]$	$[91.92,\,92.86]$	$[97.91,\,98.73]$	$[73.19,\,74.39]$
$0.5$	$98.67$	$90.48$	$95.09$	$61.12$
	$[98.27,\,99.06]$	$[89.59,\,91.38]$	$[94.55,\,95.63]$	$[60.59,\,61.64]$
$1.0$ (paste-in)	$97.48$	$89.02$	$86.23$	$50.60$

Table 2: N-Queens infill accuracy and coverage (%), final checkpoint,

750

puzzles

\times\,20

samples.

Model	$p_{\text{condclean}}$	Dropout	Best Val NLL	Checkpoint Step
$57$ M	$1.0$ (paste-in)	$0.1$	$0.4581{\scriptstyle\ \pm\ 0.0041}$	$8{,}000$
$57$ M	$1.0$	$0.2$	$0.4537{\scriptstyle\ \pm\ 0.0104}$	$12{,}000$
$57$ M	$1.0$	$0.3$	$0.4478{\scriptstyle\ \pm\ 0.0056}$	$16{,}400$
$57$ M	$1.0$	$0.4$	$0.4455{\scriptstyle\ \pm\ 0.0080}$	$19{,}200$
$57$ M	$\mathbf{0.5}$	$0.1$	$\mathbf{0.3707}{\scriptstyle\ \pm\ 0.0093}$	$23{,}600$
$132$ M	$1.0$ (paste-in)	$0.1$	$0.4573{\scriptstyle\ \pm\ 0.0022}$	$6{,}000$

Table 3: Gigaword validation NLL. (mean

\pm

std. over

5

training seeds)

Panel of Figure 4 — Figure 4: Diversity–quality frontiers. MAUVE against average response unigram entropy, traced by a softmax temperature on the denoised $x_{1}$ distribution ( $T\in[0.2,1.5]$ ). We provide as a target the human references MAUVE (estimated by scoring data halves against each other) and average unigram entropy. We note that the default dropout is $0.1$ and bars represent training seed standard deviation.

		Easy		Hard
Setting	$w$	Mean	$\Delta$ (improvement)	Mean	$\Delta$ (improvement)
$N{=}10{,}000$	$1$	$89.44$	—	$23.89$	—
		$[85.62,\,93.26]$		$[20.25,\,27.53]$
	$5$	$\mathbf{92.08}$	$+2.64$	$\mathbf{30.82}$	$+6.93$
		$[88.79,\,95.37]$	$[1.83,\,3.45]$	$[26.86,\,34.78]$	$[6.55,\,7.31]$
$N{=}1{,}000$	$1$	$1.66$	—	$0.03$	—

Table 4: Sudoku solve rate (%) under guided sampling at

p_{\text{condclean}}{=}0.2

on 2,000 held-out puzzles.

w{=}1

represents default sampling with a clean prompt during inference time.

Figure 5: Comparison to scaling dataset size. Puzzle (exact match) solve rate on Sudoku-easy using default paste-in method trained under increasing dataset sizes. All training datasets are subsets of a $100$ k training dataset. The default paste-in training objective requires $10\times$ more data to match the performance under noised prompt training $p{=}0.2$ .

Ablation	Setting	Accuracy	Coverage
Separate cond. time	Sudoku easy	$93.23$ $[91.95,94.51]$	—
	Sudoku hard	$25.09$ $[21.66,28.52]$	—
	N-Queens $n{=}8$	$97.20$ $[96.67,97.74]$	$88.84$ $[88.04,89.64]$
	N-Queens $n{=}10$	$88.56$ $[87.74,89.39]$	$51.69$ $[50.89,52.49]$
Per-token Bernoulli	Sudoku easy, $p{=}0.2$	$75.97$ $[72.89,79.05]$	—
	Sudoku easy, $p{=}0.5$	$89.75$ $[85.46,94.04]$	—

Table 5: Ablations. First: separate conditioning time variant (independent clue time

t^{\prime}

). Second: Per token noising. Third: response-only loss region, swept over

p_{\text{condclean}}

. Fourth: Fully unconditional generation. Fifth: Masked noise variant.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

	Conditioning-time clean prob. $p$
Difficulty	$0.2$	$0.5$	$1.0$
Easy	$66.95$ [64.95, 69.00]	$69.55$ [67.55, 71.60]	$68.60$ [66.60, 70.60]
Hard	$\phantom{0}4.80$ [3.90, 5.75]	$\phantom{0}5.50$ [4.55, 6.50]	$\phantom{0}3.75$ [2.95, 4.60]

Appendix

Table 6: Effect of noising the conditioning time while keeping the conditioning data clean.

p

is the probability that a conditioning tokens’s time value stays clean, i.e remains

t=1

. 95% bootstrap CIs reported.

	Sudoku		N-Queens $n{=}8$		N-Queens $n{=}10$
$p_{\text{condclean}}$	Easy Acc.	Hard Acc.	Accuracy	Coverage	Accuracy	Coverage
$0.2$	$92.38$	$24.65$	$97.13$	$89.11$	$88.93$	$52.22$
	$[90.35,94.41]$	$[16.98,32.32]$	$[96.61,97.66]$	$[88.46,89.76]$	$[87.71,90.14]$	$[51.37,53.06]$
$0.5$	$89.66$	$13.89$	$97.55$	$88.62$	$89.40$	$52.10$
	$[85.62,93.70]$	$[9.44,18.34]$	$[96.80,98.30]$	$[88.22,89.02]$	$[87.15,91.65]$	$[51.33,52.86]$
$1.0$	$61.32$	$3.84$	$97.52$	$88.54$	$88.67$	$51.92$

Appendix

Table 7: Conditioning-time-distribution with

p_{condclean}

Train pairs	$p_{\text{condclean}}$	Best Val NLL	Checkpoint Step
$191$ K	$1.0$ (paste-in)	$0.6644{\scriptstyle\ \pm\ 0.0104}$	$12{,}667$
$191$ K	$0.5$	$0.5640{\scriptstyle\ \pm\ 0.0045}$	$28{,}667$
$191$ K	$\mathbf{0.3}$	$\mathbf{0.5543}{\scriptstyle\ \pm\ 0.0054}$	$35{,}333$
$3.38$ M	$1.0$ (paste-in)	$0.4425{\scriptstyle\ \pm\ 0.0073}$	$97{,}333$
$3.38$ M	$\mathbf{0.5}$	$\mathbf{0.4133}{\scriptstyle\ \pm\ 0.0035}$	$138{,}000$
$3.38$ M	$0.3$	$0.4246{\scriptstyle\ \pm\ 0.0084}$	$128{,}667$

Appendix

Table 8: Open dialogue validation NLL. (mean

\pm

std. over

3

training seeds)

		Accuracy		Coverage
Setting	$w$	Mean	$\Delta$	Mean	$\Delta$
$n{=}8$ (length 64)	$1$	$99.43$	—	$\mathbf{92.65}$	—
		$[99.14,\,99.73]$		$[91.98,\,93.32]$
	$5$	$\mathbf{99.61}$	$+0.18$	$90.94$	$-1.71$
		$[99.37,\,99.85]$	$[0.05,\,0.31]$	$[90.42,\,91.45]$	$[-2.18,\,-1.25]$
$n{=}10$ (length 100)	$1$	$98.40$	—	$\mathbf{73.57}$	—

Appendix

Table 9: N-Queens accuracy and coverage (%) under guided sampling at

p_{\text{condclean}}{=}0.2

750

held-out boards

\times\,20

samples.

\Delta

is the paired within-seed change from

w{=}1

. Guidance improves accuracy but trades off with coverage.

	$n=12$ (length 144)
$p_{\text{condclean}}$	Accuracy	Coverage
$0.2$	$\mathbf{39.59}$	$\mathbf{58.75}$
	$[38.31,\,40.88]$	$[58.00,\,59.51]$
$0.5$	$33.49$	$51.11$
	$[31.62,\,35.36]$	$[49.44,\,52.78]$
$1.0$ (paste-in)	$22.66$	$38.62$

Appendix

Table 10: N-Queens infill accuracy and coverage (%) at

n=12

(length

144

) on a input and solution disjoint evaluation set, final checkpoint,

750

puzzles

\times\,20

samples.

Figure 6: Solution diversity at matched validity for N-Queens $n=10$ .

		Guidance weight $w$
Setting	Space	$1$	$1.5$	$2$	$3$	$5$	$8$
Easy, $N{=}10{,}000$	logit	$90.90$	$91.30$	$91.80$	$92.20$	$\mathbf{92.65}$	$\mathbf{92.65}$
Easy, $N{=}10{,}000$	prob	$90.90$	$91.00$	$91.15$	$91.35$	$91.45$	$91.55$
Hard, $N{=}10{,}000$	logit	$28.15$	$31.60$	$32.95$	$34.40$	$\mathbf{35.35}$	$34.95$
Hard, $N{=}10{,}000$	prob	$28.15$	$30.05$	$30.80$	$31.10$	$31.70$	$32.15$
Easy, $N{=}1{,}000$	logit	$2.05$	$2.45$	$3.75$	$\mathbf{4.60}$	$4.10$	$2.65$

Appendix

Table 11: Sudoku solve rate (%) over the full guidance sweep,

p_{\text{condclean}}{=}0.2

, using single seed.

	$n=8$ (length 64)		$n=10$ (length 100)
$w$	Accuracy	Coverage	Accuracy	Coverage
$1$	$99.13$	$\mathbf{92.65}$	$97.92$	$\mathbf{74.38}$
$1.5$	$99.18$ $(+0.05)$	$91.66$ $(-0.99)$	$98.75$ $(+0.83)$	$69.13$ $(-5.25)$
$2$	$99.25$ $(+0.13)$	$91.26$ $(-1.39)$	$\mathbf{98.95}$ $(+1.03)$	$67.12$ $(-7.26)$
$3$	$99.29$ $(+0.17)$	$90.85$ $(-1.80)$	$\mathbf{98.95}$ $(+1.03)$	$65.45$ $(-8.93)$
$5$	$\mathbf{99.35}$ $(+0.23)$	$91.19$ $(-1.46)$	$98.67$ $(+0.75)$	$64.22$ $(-10.16)$

Appendix

Table 12: N-Queens accuracy and coverage (%) under guided sampling,

p_{\text{condclean}}{=}0.2

, single training seed,

750

puzzles

\times\,20

samples. Parenthesised values are the change from

w{=}1

Group	Setting	Value
Model	hidden size / blocks / heads	$512$ / $8$ / $8$ (default), $768$ / $12$ / $12$ (Gigaword 132M)
	cond. dim / dropout	$128$ / $0.1$
	board length	$81$ (Sudoku), $64$ / $100$ (N-Queens $n{=}8$ / $10$ ), $80$ (Gigaword)
Algorithm	pred. type	$x_{1}$
	loss type	flow
	$p_{\text{condclean}}$	$\{0.1,0.2,0.3,0.5,1.0\}$ (Sudoku),

Appendix

Table 13: Shared hyperparameters

Explore similar work

Reasoning with Continuous Latent Diffusion
Sep 28, 2026Xiang ChengEfficient Latent Reasoning Latent Flow
Duke University Department of Electrical and Computer Engineering
Let It Go or Learn to Self-Correct: Continuous Diffusion for Constrained Discrete Tasks
Sep 8, 2026Mariia Drozdova, Stéphane Liem Nguyen, François FleuretDenoising Diffusion Probabilistic Model Diffusion Models
University of Geneva
Hierarchical Continuous Diffusion Language Models
Oct 1, 2026Hui Ren, Zihan Li, Chang Liu +2Diffusion Language Models Diffusion Models
University of Illinois Urbana-Champaign · Amazon.com, Inc.

Sep 28, 2026, cs.AIJ/K move · Enter open · S save

Reasoning with Continuous Latent Diffusion

Xiang Cheng

Duke University Department of Electrical and Computer Engineering

Efficient Latent Reasoning Latent Flow Diffusion Models Sentence Encoders

Open paper AskPDF arXiv

Continuous diffusion generates complete reasoning solutions through iterative refinement in latent space. We introduce the Continuous Embedding Diffusion Reasoner (CEDR), an ELF-based training and inference recipe. Our experiments show that accurate decoding alone does not ensure strong reasoning performance. We therefore learn compact representations from multiple layers of a strong autoregressive teacher. Their decomposition also enables asynchronous denoising at different rates. We show that prompt encodings need only preserve the information required for the correct text-conditional score, rather than exactly match teacher features, and use a staged curriculum to learn a compact prompt encoder that replaces the teacher Transformer at inference. We adapt DiffusionNFT to learned self-conditioning guidance and incorporate gold-solution endpoints to supplement sparse rewards. Our supervised models outperform reported results from recent continuous-diffusion baselines at comparable backbone scales on mathematical reasoning and HumanEval code generation. With a 638M-parameter denoising backbone and learned prompt conditioning, post-NFT CEDR-L achieves 63.74% pass@1 on GSM8K and 24.6% on MATH500 at 64 denoising steps, and 32.85% on HumanEval and 30.18% on HumanEval+ at 128 denoising steps. Code will be available at: https://github.com/chengxiang/CEDR.

Abstract

Explore similar work

Reasoning with Continuous Latent Diffusion

Let It Go or Learn to Self-Correct: Continuous Diffusion for Constrained Discrete Tasks

Hierarchical Continuous Diffusion Language Models