Value-Informed Schedule Trimming for Accelerated Sequential Monte Carlo Guidance in Discrete Diffusion

Jaehyeon Kim; Ziseok Lee; Siyoung Choi; Kyungsu Kim

cs.AIOct 14, 2026

Value-Informed Schedule Trimming for Accelerated Sequential Monte Carlo Guidance in Discrete Diffusion

Authors: Jaehyeon Kim, Ziseok Lee, Siyoung Choi, Kyungsu Kim

Organizations: Seoul National University

Abstract

Reward-guided discrete diffusion enables test-time alignment with downstream objectives, but applying Sequential Monte Carlo (SMC) guidance at every denoising step is computationally expensive. Active guidance steps require additional reward evaluations and, for gradient-based proposals, value-gradient computations. Sparse guidance reduces this cost by guiding only a subset of timesteps, but commonly used schedules are fixed heuristics whose effectiveness can vary substantially across tasks. We propose VISTA, a training-free method that automatically selects guided timesteps under a fixed budget. VISTA formulates sparse guidance as approximation of the ideal full-guidance probability path and derives an estimable upper bound on $\ell_1$ path deviation. Using value statistics collected from a small number of full-guidance warmup generations, VISTA optimizes the resulting empirical surrogate exactly via dynamic programming. The warmup generations can be retained as model outputs, and after schedule selection VISTA has the same per-generation guidance complexity as other sparse schedules with the same budget. Across text, biological sequence, and image generation tasks, VISTA discovers task-dependent schedules and outperforms hand-designed sparse schedules in most tested settings, while approaching or exceeding full-guidance performance on several task metrics. In toxic-text generation, for example, VISTA attains a 0.99 unique-toxic ratio compared with 1.00 for full guidance while reducing post-selection per-generation latency from 204.23 s to 38.16 s, a 5.35 $\times$ speedup.

Figures & tables

Method	Discrete	Reward	Theoretical Guarantee
Adaptive Guidance [ 4 ]	×	×	×
FasterCache [ 23 ]	×	×	×
Tortoise-and-Hare [ 20 ]	×	×	✓
Guidance Interval [ 18 ]	×	×	×
VISTA (Ours)	✓	✓	✓

Table 1: Comparison of VISTA with existing guidance acceleration methods. Discrete: Designed for discrete state spaces; Reward: Handles external reward functions; Theoretical Guarantee: Provides a rigorous theoretical justification for the acceleration schedule.

Figure 1: Impact of guidance schedules on particle distributions. A minimal schedule (e.g.,

\mathcal{G}=\{0\}

) is asymptotically correct as

N\to\infty

, but with finite particles, it leads to diversity collapse through the duplication of a few terminal particles. In contrast, full guidance (

\mathcal{G}=\mathcal{T}

) maintains intermediate marginals close to the reward-tilted path, ensuring both high reward and sample diversity.

Variant	Full Guidance	Sparse Guidance
SMC-base	$NT\times p,\ NTJ\times r$	$NT\times p,\ NT^{\prime}J\times r$
SMC-grad	$NT\times p,\ NTJ\times r,\ NT\times\nabla v$	$NT\times p,\ NT^{\prime}J\times r,\ NT^{\prime}\times\nabla v$

Table 2: Per-generation cost after schedule selection. Here,

p

is a pretrained reverse-model evaluation,

q

is an amortized proposal,

r

is a reward-model evaluation,

\nabla v

is a value-gradient evaluation,

N

is the number of particles,

T

is the diffusion horizon,

T^{\prime}

is the guidance budget, and

J

is the number of rollout samples for value estimation (see Algorithm 5 for details).

Panel of Figure 2 — Figure 2: Binary MNIST (SMC-grad). Execution time, Unique Valid, and UTD as the guidance budget $T^{\prime}$ varies.

Panel of Figure 3 — Figure 3: Toxic Text (SMC-grad). Execution time, Unique Toxic Ratio, and $\hat{S}(\mathcal{G})$ as the guidance budget $T^{\prime}$ varies.

Panel of Figure 4 — Figure 4: CIFAR-10 (SMC-base). Execution time, unique valid samples, and $\hat{S}(\mathcal{G})$ as the guidance budget $T^{\prime}$ varies.

Table 7

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Experiment	ESS threshold	Partial resampling	Systematic resampling
Binary MNIST	0.95	$\lfloor N/2\rfloor$	Yes
Toxic Text	0.98	$N$	Yes
CIFAR-10	0.95	$\lfloor N/2\rfloor$	Yes
DNA Design	0.98	$\lfloor N/2\rfloor$	Yes
Protein Fitness	0.98	$\lfloor N/2\rfloor$	Yes
Continuous MNIST	0.98	$\lfloor N/2\rfloor$	Yes

Appendix

Table 5: Resampling configurations for each experiment. Adaptive resampling is triggered when the normalized Effective Sample Size (ESS

/N

) falls below the specified threshold. Partial resampling denotes the number of particles replaced at each resampling step.

Panel of Figure 6 — Figure 6: Binary MNIST (SMC-base). Execution time, unique valid samples, and UTD as the guidance budget $T^{\prime}$ varies.

Table 10

Panel of Figure 7 — Figure 7: VISTA schedules $\mathcal{G}$ for varying $T^{\prime}$ on Binary MNIST

$T^{\prime}$	Policy	Time [s] $\downarrow$	Unique Toxic Ratio $\uparrow$	$\hat{S}(\mathcal{G})$ $\uparrow$
100	Full	$204.23\pm 0.65$	$\mathbf{1.00\pm 0.02}$	$\mathbf{0}$
5	Interval 1	$14.10\pm 0.20$	$0.74\pm 0.34$	$68.97$
	Interval 2	$15.08\pm 0.32$	$0.73\pm 0.28$	$55.61$
	Interval 3	$15.01\pm 0.25$	$0.72\pm 0.35$	$34.85$
	Interval 4	$15.15\pm 0.35$	$0.69\pm 0.42$	$23.60$
	Interval 5	$14.34\pm 0.25$	$0.05\pm 0.17$	$5.16$

Appendix

Table 8: Toxic text generation (SMC-grad).

Figure 8: VISTA schedules

\mathcal{G}

for varying

T^{\prime}

(Toxic Text, SMC-grad)

$T^{\prime}$	Policy	Time [s] $\downarrow$	Unique Valid $\uparrow$	$\hat{S}(\mathcal{G})$ $\uparrow$
1000	Full	$43.51\pm 0.07$	$\mathbf{2.18\pm 1.02}$	${--}$
5	Interval 1	$20.03\pm 0.04$	$0.88\pm 0.46$	$36.77$
	Interval 2	$19.99\pm 0.03$	$1.02\pm 0.22$	$329.40$
	Interval 3	$19.98\pm 0.01$	$0.72\pm 0.26$	$276.90$
	Interval 4	$19.98\pm 0.02$	$0.64\pm 0.28$	$155.30$
	Interval 5	$19.98\pm 0.02$	$0.60\pm 0.30$	$21.21$

Appendix

Table 9: CIFAR-10 class-conditional generation: execution time, unique success count, and

\hat{S}(\mathcal{G})

Figure 9: VISTA schedules

\mathcal{G}

for varying

T^{\prime}

(CIFAR-10, SMC-base)

Figure 10: VISTA schedules

\mathcal{G}

for varying

T^{\prime}

(DNA, SMC-grad)

Figure 11: VISTA schedules

\mathcal{G}

for varying

T^{\prime}

(Protein Fitness, MDM, SMC-base)

$T^{\prime}$	Policy	Time [s] $\downarrow$	Unique Valid $\uparrow$	$\hat{S}(\mathcal{G})$ $\uparrow$
128	Full	$3.26$	$\mathbf{3.15\pm 2.37}$	–
16	Interval 1	$1.42$	$4.45\pm 3.19$	$2.71\times 10^{3}$
	Interval 2	$1.41$	$7.50\pm 3.72$	$6.05\times 10^{3}$
	Interval 3	$1.41$	$6.10\pm 3.93$	$7.86\times 10^{3}$
	Interval 4	$1.41$	$5.20\pm 2.84$	$3.53\times 10^{3}$
	Interval 5	$1.41$	$2.20\pm 1.20$	$602.24$

Appendix

Table 10: Protein fitness generation, Uniform Discrete Diffusion (SMC-base, 32 particles

\times

20 runs): execution time, unique valid count, and

\hat{S}(\mathcal{G})

$T^{\prime}$	Policy	Time [s] $\downarrow$	Unique Valid $\uparrow$	$\hat{S}(\mathcal{G})$ $\uparrow$
100	Full	$15.47\pm 0.08$	$\mathbf{10.33\pm 3.45}$	–
6	Interval 1	$4.29\pm 0.20$	$1.93\pm 1.44$	$0.06$
	Interval 2	$4.24\pm 0.03$	$1.60\pm 1.25$	$0.36$
	Interval 3	$4.24\pm 0.02$	$7.77\pm 4.64$	$3.40$
	Interval 4	$4.25\pm 0.03$	$12.87\pm 6.77$	$5.08$
	Interval 5	$4.15\pm 0.03$	$1.73\pm 1.28$	$0.11$

Appendix

Table 11: MNIST (TDS, reproduce full/sparse): execution time, unique valid count, and

\hat{S}(\mathcal{G})

Figure 12: Optimized guidance schedules

\mathcal{G}

for varying

M

(Binary MNIST, SMC-base)

Figure 13: Optimized guidance schedules

\mathcal{G}

for varying

M

(Binary MNIST, SMC-grad)

Figure 14: Optimized guidance schedules

\mathcal{G}

for varying

M

(Toxic Text, SMC-grad)

Figure 15: Optimized guidance schedules

\mathcal{G}

for varying

M

(CIFAR-10, SMC-base)

Figure 16: Optimized guidance schedules

\mathcal{G}

for varying

M

(DNA, SMC-grad)

Figure 17: Optimized guidance schedules

\mathcal{G}

for varying

M

(Protein Fitness, SMC-base, MDM)

Figure 18: Optimized guidance schedules

\mathcal{G}

for varying

M

(Protein Fitness, SMC-base, UDM)

Figure 19: Optimized guidance schedules

\mathcal{G}

for varying

M

(MNIST, TDS)

Inference-Time Guidance

Inference-time guidance steers pretrained generative models, language models, and policies toward desired outputs without requiring full retraining.

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Apr 8, 2026

VASR: Variance-Aware Systematic Resampling for Reward-Guided Diffusion

Sequential Monte Carlo (SMC) samplers for reward-guided diffusion models often suffer from rapid lineage collapse: a few high-reward particles dominate the population within a handful of resampling steps, destroying diversity and degrading sample quality. We propose a variance-decomposition framework for reward-guided diffusion SMC that separates continuation variance

V_t^{\mathrm{cont}}

from residual variance

V_t^{\mathrm{res}}

, revealing that high offspring-count variance under the commonly used multinomial resampling drives this collapse. This motivates VASR (Variance-Aware Systematic Resampling), which addresses both variance terms via variance-optimal mass allocation

m_t \propto w_t e^{r_t}

(minimizing

V_t^{\mathrm{cont}}

) and systematic resampling (controlling

V_t^{\mathrm{res}}

). For latent diffusion models where intermediate rewards are noisy due to stochastic continuations, we propose VASR-Max, a deliberately biased high-selection variant for variance-sensitive reward optimization. Both methods are training-free, fully parallelizable, and add only linear overhead. On MNIST and CIFAR-10, VASR achieves as high as

26\%

better FID than prior SMC methods while remaining 66 times faster than MCTS-based value methods at matched compute. On text-to-image generation, VASR-Max consistently outperforms the strongest SMC baseline across compute budgets and matches MCTS-based methods within 2.5--3% reward at high budgets while being approximately times faster.

Shivanshu Shekhar, Sagnik Mukherjee, Jia Yi Zhang +1

Siebel School of Computing and Data Science University of Illinois Urbana-Champaign · Department of Statistics University of Illinois Urbana-Champaign

Diffusion Model Sampling Diffusion Sampling Diffusion Model Guidance

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Aug 27, 2026

VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusion

Masked discrete diffusion models perform strongly on text, code, and biological sequences, but their training objective rewards only naturalness, and retraining the generator for every new reward is expensive. Inference-time steering of a frozen model either guides the sampler by the reward gradient or searches over several trajectories, and recent samplers combine the two. Such combinations are assembled as pipelines that leave three choices at their defaults: a guidance estimate resting on one Gumbel draw per sample, a reward tilting placed without reference to the distribution the combination then targets, and a selection temperature held fixed although the spread of per-step rewards drifts. We identify that distribution and settle the three choices against it. We therefore propose Variance-reduced Guidance and Adaptive Selection (VGAS), a simple yet effective inference-time framework that reduces the variance of the guidance estimate for both reward types, applies the reward tilting in the clean-token logits, where the pretrained schedule is preserved, and sets the selection temperature per step. Across regulatory DNA, protein and small-molecule benchmarks, VGAS attains the best training-free reward and matches or surpasses a reward-fine-tuned generator.

Kwanyoung Kim

Department of AI, GIST

Diffusion Model Alignment Diffusion Model Guidance Masked Diffusion Models Inference-Time Guidance

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Oct 1, 2026

Learned End-to-End Guidance Schedules for Diffusion Models

Diffusion models are a powerful generative paradigm used across multimedia and scientific applications. Guided diffusion methods impose requirements on the generation by adding the gradient of a differentiable loss (the guidance function) as a drift term during inference. The weight of this drift (the guidance scale) is critical for the trade-off between data quality and requirement satisfaction. To achieve both of these goals, guided diffusion must resort to small guidance scales and lengthy sampling, incurring high computational costs. This work proposes learned end-to-end guidance schedules (LEEGS) to achieve these objectives with fewer sampling steps. LEEGS trains a time-dependent schedule by minimizing the guidance function over a small set of examples using stochastic gradient descent. Backpropagating through guided sampling is computationally expensive, so LEEGS uses an approximation of the gradient that cuts training time by a factor of 4. We evaluate LEEGS on diverse guidance tasks, including (a) image inpainting, (b) noisy image inverse problems, (c) face-ID-guided generation, and (d) forward and inverse PDE problems, outperforming baselines at equal budget (50 or 100 NFEs), or matching constant guidance with only 10% of the steps.

Aneesh Barthakur, Mathias Niepert, Luiz F. O. Chamon

University of Stuttgart · École polytechnique, Institut Polytechnique de Paris

Diffusion Model Guidance Few-Step Diffusion Sampling Diffusion-Based Inverse Problems

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Abstract

Inference-Time Guidance

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