Source-linked AI summary

LatticeSMC: Where to Spend Inference-Time Compute in Chunked Sequence Generators

Xuanchen Wang, Heng Wang, Weidong Cai

arXiv:2610.02774v1cs.LG

TL;DR

Long-form generators create sequences chunk by chunk, while rewards often concern the full sequence, and existing steering methods place compute along only one axis. LatticeSMC uses a two-axis Feynman–Kac model and exact telescoping results to guide steering under matched compute. At 32 particles, it improves reported beat alignment and prompt adherence while preserving held-out quality.

  • Problem

    Existing steering methods act along one axis and are often compared under unmatched compute or different return rules, despite rewards applying to full sequences generated chunk by chunk.

    Source: §1 · p. 2
  • Method

    LatticeSMC uses chunk-axis potentials in a two-dimensional Feynman–Kac model, with exact telescoping results for chunk-additive rewards and terminal rewards with prefix scores.

    Source: §1 · p. 2, §3.4 · p. 5
  • Results

    At 32 particles, beat alignment rises from 0.234 to 0.441 and prompt adherence from 0.470 to 0.560 under matched compute, while held-out quality is preserved.

    Source: §1 · p. 2
  • Takeaways & Limitations

    Commitment should track information in the current potential, while lookahead’s value is predicted by within-set predictability of future reward.

    Source: §6 · p. 10

    The horizon study is on dance, the human study covers two rewards, and the propositions fix the target but not finite-particle behavior.

    Source: §6 · p. 10

Abstract

from arXiv · show

Long-form generators for music, motion and video produce sequences chunk by chunk, with each chunk generated by iterative denoising while rewards are defined over the full sequence. Existing inference-time steering methods typically act on one axis at a time: best-of-N at the end, Feynman-Kac steering across denoising steps, or streaming pruning across chunks, and are often compared under unmatched compute or different return rules. We introduce budget-matched chunked steering and propose LatticeSMC, a sampler derived from a Feynman-Kac model on the two-dimensional lattice of chunk index and denoising step. Two telescoping results make its design exact: for chunk-additive rewards, the two axes induce identical weights, so resampling should occur where lookahead is cheapest; for terminal rewards, any prefix score defines an exact intermediate potential, making prefix-evaluable rewards twists with no estimation or extra denoiser calls. LatticeSMC resamples on these potentials at chunk boundaries and, when scoring is free, within chunks, returning either a weighted draw or the best particle. Under matched compute, on music-to-dance diffusion and 40-second text-to-music generation, it raises beat alignment from 0.234 to 0.441 (best-of-N: 0.354) and prompt adherence from 0.470 to 0.560 at 32 particles, while preserving held-out quality. It also retains its advantage on long-range rewards and is preferred by human raters in 60-77 percent of pairwise comparisons. Finally, we show that commitment strength should follow the information in the current potential, while the value of lookahead is predicted by the within-set predictability of future reward.

1 INTRODUCTION

Long-form generators produce sequences in chunks, but rewards often concern the full sequence, leaving inference-time methods without a principled, budget-matched rule for where to steer. LatticeSMC uses a two-axis Feynman–Kac formulation and exact telescoping results to guide that choice.

Motivation

  • Existing methods steer at one stage—end-of-sequence, denoising steps, or chunk boundaries—and comparisons have used unmatched budgets or return rules.The resulting choice of where to resample on the chunk-and-denoising lattice lacks a principled answer.Source: §1 · p. 2

Contribution

  • The paper models inference-time steering as potentials on a lattice of chunk index and denoising step, with telescoping identities for chunk-additive and terminal rewards.For additive rewards, both axes yield identical weights; for terminal rewards, prefix scores give exact intermediate potentials.Source: §1 · p. 2
  • LatticeSMC is a training-free sampler with no learned components, using potentials prescribed by the lattice model.It returns either a weighted draw or the best particle.Source: §1 · p. 2
  • The paper proposes setting commitment according to information in the current potential and allocating lookahead according to within-set predictability of future reward.Prefix-evaluable scores provide such predictability, whereas learned regressors do not.Source: §1 · p. 2

Results

  • With 32 particles, LatticeSMC raises beat alignment from 0.234 to 0.441 and prompt adherence from 0.470 to 0.560 while preserving held-out quality.It matches or outperforms every compared method on every reward under matched compute.Source: §1 · p. 2

2 RELATED WORK

Prior work studies inference-time search, reward-guided diffusion, SMC, and streaming generation, often along a single generation axis. LatticeSMC brings the chunk axis into the placement problem for inference-time compute.

Inference-Time Compute and Search

  • Inference-time search methods use repeated sampling, verification, tree search, or adaptive sampling and revision, while analogous diffusion methods search noises or trajectories or guide test-time alignment.These approaches operate on a single generation clock.Source: §2 · p. 3

Reward-Guided Diffusion Sampling

  • Reward-guided diffusion includes kernel modification, reward-specific fine-tuning, and population reweighting; LatticeSMC belongs to the population-based family.Its contribution is to add the chunk axis and characterize placement at matched cost.Source: §2 · p. 3

Sequential Monte Carlo

  • LatticeSMC builds on bootstrap filtering, adaptive resampling, low-variance resampling, and classical twisting toward expected future weight.The paper connects twisting’s usefulness to within-set predictability of future reward.Source: §2 · pp. 3–4

Chunked and Streaming Generators

  • Video, music, and dance systems generate or refine successive blocks, whereas this paper asks where to spend inference-time compute across chunk and denoising axes.Examples include streaming video pruning [Tu et al., 2026] and latent-diffusion music inpainting (Evans et al., 2024; 2025).Source: §2 · p. 4

3 THE LATTICE FEYNMAN-KAC MODEL

The paper formulates chunked steering as a Feynman–Kac model over chunk index and denoising step, then derives exact potentials and a sampler for budget-matched inference. Its telescoping results specify when the axes give the same weights and how prefix scores can guide terminal rewards.

3.1 BUDGET-MATCHED CHUNKED STEERING

  • Budget-matched chunked steering returns a sequence under a denoiser-evaluation budget, targeting either reward-tilted sampling or reward maximization.A generator produces chunks through iterative denoising; rewards may be chunk-additive or available only on complete sequences.Source: §3.1 · p. 4

3.2 THE LATTICE

  • The lattice Feynman–Kac model attaches nonnegative potentials to intermediate chunk-and-denoising states, with their product defining the reward-tilted target.Sequential Monte Carlo follows the base kernels, accumulates potential weights, and resamples when effective sample size falls below a threshold.Source: §3.2 · p. 4

3.3 TWO TELESCOPING RESULTS

  • For chunk-additive rewards, denoising-axis potentials telescope to the chunk potential, so both axes give the same path measure and per-chunk weights.For terminal rewards, prefix-score potentials with a terminal correction preserve the target for any prefix scores; prefix-evaluable rewards need no estimation for this twist.Source: §3.3 · p. 5

3.4 LATTICESMC

  • LatticeSMC applies chunk-end potentials and systematically resamples when ESS < N/2, optionally adding within-chunk events when plug-in scoring is free.It returns a weighted draw for sampling or the highest-reward particle for search; its cost includes NKS denoiser evaluations, KN reward evaluations, and, for latent generators, KN decoder calls.Source: §3.4 · p. 5

4 EXPERIMENTS AND RESULTS

The experiments compare chunked steering methods under matched denoiser-evaluation budgets across dance diffusion and 40-second text-to-music. LatticeSMC improves reward against terminal selection and pruning in the reported settings, while the return rule, reward timing, and scoring cost shape which schedule is advantageous.

4.1 SETUP

  • The evaluation covers chunked dance diffusion and 40-second text-to-music, with four sequence-level rewards and matched denoiser-evaluation budgets.Dance uses beat alignment and long-range repetition; music uses prompt adherence and motif recurrence. Prefix scoring on music costs one decode and one CLAP pass.Source: §4.1 · p. 6

4.2 CHUNK-AXIS RESAMPLING IS THE COMPUTE-EFFICIENT PLACEMENT

  • At N = 32, chunk-boundary LatticeSMC beats terminal selection across four rewards and exceeds pruning under matched return rules.With argmax return, beat alignment is 0.441 versus 0.354 for best-of-N, and prompt adherence is 0.560 versus 0.530. Held-out dance quantities stay inside base-model intervals; on music, tempo, aesthetics, and seam continuity stay within 6% of base, while high-frequency energy and embedding diversity decline under every steering method.Source: §4.2 · p. 7

4.3 THE RETURN RULE IS WORTH AS MUCH AS THE RESAMPLING SCHEME

  • At N = 32, switching from a weighted draw to the best particle adds 0.012 to 0.042, with gains growing as particle count increases.Pruning leads at the smallest budgets on beat alignment and prompt adherence, but LatticeSMC with argmax crosses it by N = 32 on every reward and earlier on motif recurrence, prompt adherence, and repetition.Source: §4.3 · pp. 7–8

4.4 TILT, HORIZON, TEMPERATURE AND COST

  • For late-arriving rewards, ESS-gated resampling outperforms top-M replication, while horizon changes require per-boundary tilt adjustment for beat alignment.On the long-range repetition reward, the boundary schedule leads pruning by +0.100 at K = 6 and +0.121 at K = 8. For sequence-normalized rewards, the tilt to hold fixed across horizons is α ∝ 1/K.Source: Table 3 · p. 8, §4.4 · pp. 8–9
  • On music, dense within-chunk scoring uses four times the boundary schedule’s decoder calls and 3.6 times its wall-clock for the same reward.At N = 32, the schedules use 512 versus 128 decoder calls.Source: §4.4 · p. 9

4.5 HUMAN EVALUATION

  • Human raters prefer LatticeSMC to the base model, best-of-N, and chunk pruning on reward judgments, with all reported intervals above 50%.Across the two testbeds, preference over comparators ranges from 66.0% to 77.0% on the reward question; overall-question win rates are 60.5% to 69.0%.Source: §4.5 · p. 9

5 ANALYSIS: WHEN CONTENT-AXIS LOOKAHEAD PAYS

Lookahead helps only when prefixes distinguish future rewards within a particle set, so cross-condition predictability alone can mislead. The design rule is to use exact prefix scores when available and validate estimated twists by within-set ranking and weight error.

5.1 WHAT A TWIST CAN KNOW IS A WITHIN-SET QUANTITY, AND SO IS ITS ACCURACY

  • For beat alignment, the between-prefix share of exp(Sk/α) was at most 0.14, while prompt prefixes explained 0.47, 0.62, and 0.66 of terminal variance after one, two, and three chunks.Repetition had a pooled share of 0.9, but same-condition rollout targets spread by 2.9 nats, about 2 nats of which were Monte Carlo error at M = 4.Source: §5.1 · p. 9
  • Within-set predictability ρk measures the share of future-reward variation attributable to prefix means rather than rollout noise.The analysis estimates it from base-model rollouts and distinguishes it from pooled, between-condition predictability.Source: §5.1 · p. 9
  • A rollout-trained regressor with cross-prompt R2 of 0.90 ranked repetition particles almost randomly, correlating −0.04 after chunk one and 0.35 after chunk two with the oracle twist.Its residual was 4.3 nats on fresh prefixes and 6.0 nats within a set; applying it lowered reward by 0.05 on the 4M model and 0.02 on the 38M model relative to ψ ≡1 at N = 32.Source: §5.1 · p. 10, Table 4 · p. 10

5.2 A DESIGN RULE

  • Use exact prefix-evaluable rewards as twists without estimation or extra denoiser cost; charged rollouts set headroom but lose to additional particles at matched cost for M ≤4.The design rule is to measure ρk first, omit lookahead when it is small, and validate estimated twists by within-set correlation and residual in nats rather than cross-prompt fit.Source: §5.2 · p. 10

6 DISCUSSION AND CONCLUSION

The discussion frames chunked steering as one lattice Feynman–Kac model, with telescoping identities fixing the target and reward information guiding commitment and lookahead. The appendix proofs establish these identities and explain why denoising-axis plug-in scores are least informative early in a chunk.

6 DISCUSSION AND CONCLUSION

  • LatticeSMC ties or leads the compared methods at matched compute across four rewards, two model sizes, and three horizons, and human evaluators prefer its outputs.The conclusion recommends boundary commitment proportional to the exact potential’s information and lookahead proportional to within-set future-reward predictability.Source: §6 · p. 10
  • The horizon study is limited to dance, the dance generators are small study-trained models, and the human study covers two rewards.Gradient guidance is not compared, and a bound relating ρk to incremental-weight variance remains open; the music generator’s 40-second context does not carry prompted tempo over 80 seconds.Source: §6 · p. 10

A.1 PROOFS

  • For chunk-additive rewards, denoising-step log-potentials telescope to the exact chunk reward weight along every lineage, regardless of resampling events.Across chunks, the product is exp(r(x)/α), so the two models share the same path measure and differ only in admissible resampling times.Source: §A.1 · p. 16
  • For terminal rewards, the log-potentials telescope to exp(r/α) up to a trajectory-independent constant, preserving the target path measure.Setting β = 0 leaves only a terminal potential and recovers best-of-N importance sampling.Source: §A.1 · p. 16

A.2 THE PLUG-IN POTENTIAL AND THE OPTIMAL TWIST

  • Denoising-axis plug-in lookahead is least informative early, as conditional uncertainty in the current chunk is largest then, and becomes exact at the final denoising step.The proposition fixes the chunk-end weight, but not finite-particle behavior of intermediate resampling.Source: §A.2 · p. 16

A.4 EXISTING METHODS AS LATTICE PLACEMENTS

The appendix describes existing steering methods as different placements of potentials or resampling on the chunk-by-denoising lattice. Its algorithm uses a shared particle loop, optional dense resampling, and either weighted-draw or argmax return.

A.4 EXISTING METHODS AS LATTICE PLACEMENTS

  • LatticeSMC advances each particle through chunks and denoising steps, optionally applying dense intermediate potentials and ESS-gated systematic resampling.At boundaries it applies the remaining chunk-term or prefix-score increment, then resamples when ESS < N/2.Source: §A.4 · p. 17
  • The sampler returns either a categorical draw from normalized particle weights or the particle with the highest reward.Best-of-N importance resampling and argmax share their particle set and differ only in the final index.Source: §A.4 · p. 17
  • Best-of-N applies a terminal potential, Feynman–Kac steering resamples at selected denoising steps, chunk pruning replicates top-M prefixes at boundaries, and LatticeSMC uses exact chunk or prefix-score potentials.The compared methods share the same kernels and per-slot noise streams.Source: Table 5 · p. 16, §A.4 · p. 17

A.5 IMPLEMENTATION DETAILS

Implementation details specify reproducibility, accounting, and temperature choices, while the lookahead appendix compares exact scores, rollouts, and learned predictors. Within-set predictability is estimated by separating variation in prefix means from rollout noise.

A.5 IMPLEMENTATION DETAILS

  • Runs are reproducible from seeded particle-slot noise streams, and repeated runs with the same seed produce bitwise-identical particle systems.A sampler with all potentials set to one reproduces the base sampler bitwise; proposition checks found maximum log-potential discrepancy below 10−13 in double precision.Source: §A.5 · pp. 17–18
  • The denoiser-evaluation counter charges each forward-call row, including doubled batches for classifier-free guidance, while decoder calls and reward evaluations are counted separately.Reported counts are audited against NKS times the guidance multiplicity.Source: §A.5 · p. 17
  • Music temperature is set from base-sample reward spread, while dance reports the full α sweep of 0.2, 0.05, and 0.02.On music, α = Δ/ln 103; the dance settings imply maximum weight ratios of 3, about 80, and about 104 across 32 particles.Source: §A.5 · p. 18

B LOOKAHEAD: MEASUREMENTS AND TWIST DETAILS

  • Exact prefix scores add no estimation or denoiser cost and raise terminal CLAP by 0.020 at N = 32, whereas rollouts add +0.058 on repetition but lose to extra particles at matched cost for M ≤4.Learned predictors’ rollout-derived targets have about 2 nats of Monte Carlo error against a within-set spread of about 3 nats.Source: B LOOKAHEAD: MEASUREMENTS AND TWIST… · p. 18

B.1 ESTIMATING WITHIN-SET PREDICTABILITY

  • Within-set predictability ρk estimates the fraction of future-reward variance explained by prefix means after correcting their variance for finite-rollout noise.The estimator subtracts the mean per-prefix sample variance divided by M from the variance of prefix means, then divides by the corrected between-prefix variance plus within-prefix variance.Source: §B.1 · p. 18

B.2 WITHIN-SET ACCURACY OF A TWIST

A learned twist must rank future reward within a particle set, because set-level offsets cancel in normalized weights. The reported regressor’s residual is mostly within-sequence, while tempering reduces its influence without improving its within-set accuracy.

B.2 WITHIN-SET ACCURACY OF A TWIST

  • The within-set accuracy measure correlates candidate and oracle log twists across particles, while its weight-level error removes the set mean.The set mean cancels in normalized weights.Source: §B.2 · p. 18
  • 73% of the learned twist’s held-out error is within-sequence, the component that does not cancel in normalized particle weights.The regressor’s within-set residual standard deviation is 6.0 nats.Source: §B.2 · p. 19

B.3 TWIST VARIANTS THAT RESCALE SIGNAL AND NOISE TOGETHER

  • Tempering the regressor reduces its reward penalty from −0.053 to near zero, but its within-set correlation remains unchanged.At β = 0.25 and 0.1, the reward differences (+0.003 and −0.002) are indistinguishable from ψ ≡1.Source: §B.3 · p. 19

B.4 ROLLOUT LOOKAHEAD AT MATCHED COST

  • At matched cost, rollout twists trail the exact-potential sampler on repetition across the tested particle counts and rollout budgets.The oracle twist’s +0.058 gain requires 8,000 denoiser evaluations per particle, 20 times the 400 evaluations for the sequence itself.Source: §B.4 · p. 20

B.5 DENOISING-AXIS PLUG-IN ACCURACY

  • For chunk-local rewards, denoising-axis plug-in predictions become accurate late in denoising and are exact at the chunk’s end.Within-chunk resampling changes resampling times, while the chunk weight remains exact when scoring is free.Source: §B.5 · p. 20

C.1 TESTBEDS

  • The testbeds pair dance diffusion with beat alignment and long-range repetition, and 40-second text-to-music generation with prompt adherence and motif recurrence.Dance chunks use a clean prefix and a generated chunk; music is generated in four 10-second chunks, with prefix scoring requiring a decode and CLAP pass.Source: §C.1 · pp. 20–21, Figure 4 · p. 21

C.2 REWARDS AND HELD-OUT METRICS

The section defines four sequence rewards and held-out quality measures, then compares inference methods across compute costs and pruning strengths. LatticeSMC’s schedules can have different costs, and pruning’s relative performance changes with particle count and reward.

C.2 REWARDS AND HELD-OUT METRICS

  • Beat alignment averages beat-to-motion timing scores, while repetition compares each dance chunk with chunk k −2 and sums those pairwise rewards.The additive and full repetition rewards coincide exactly.Source: §C.2 · pp. 21–22
  • Prompt adherence measures CLAP similarity between the prompt and full clip; motif recurrence compares CLAP embeddings of the fourth and first 10-second windows.The motif prefix score is available at the last boundary.Source: §C.2 · p. 22
  • Held-out measures cover dance realism, contact, travel and diversity, and music tempo, high-frequency energy, aesthetics, seam continuity and embedding diversity.None is used by any steering method.Source: §C.2 · p. 22

C.3 COST ACCOUNTING AND COMPUTE

  • Compute accounting tracks denoiser rows, decoder calls, reward evaluations and wall-clock time; the main study used about 250 GPU-hours, plus about 110 for additional runs.Wall-clock ratios are informative because processes shared a GPU.Source: §C.3 · pp. 22–23

C.4 TEMPERATURE, COST AXES AND CROSSOVER

  • Best-of-N is cheapest per particle and lowest in reward at every budget, while the dense music schedule uses 3.6× more decoder calls than the boundary schedule.The boundary and dense schedules coincide on denoiser evaluations; the dense schedule’s curve flattens from N = 8.Source: Figure 6 · p. 23
  • ESS-gated resampling overtakes pruning between N = 16 and 32 on beat alignment, at N = 8 on prompt adherence, and at N = 4 on motif recurrence.It leads from N = 4 on long-range repetition; the 38M model reproduces the 4M crossovers.Source: Figure 7 · p. 23

C.5 PRUNING STRENGTH

  • Chunk pruning retains the top M particles by prefix reward and expands each into N/M continuations; the study compares pruning strengths at matched budgets.Table 7 reports paired differences, bootstrap intervals and held-out quantities.Source: §C.5 · p. 24, Table 7 · p. 24

C.6 HORIZON AND PER-CHUNK TILT

Longer dance horizons preserve the boundary schedule’s lead on repetition, while beat-alignment results depend on the per-chunk tilt. The music model’s 80-second horizon was not evaluated because its rolling-context base failed the pre-set tempo-adherence gate.

C.6 HORIZON AND PER-CHUNK TILT

  • The dance K = 8 evaluation used only 16 conditions with sufficiently long recordings, while K = 6 covered all 40 conditions.The long-range repetition reward sums over K −2 chunk pairs.Source: §C.6 · p. 24
  • For chunk-additive beat alignment, keeping per-boundary tilt fixed as the horizon grows weakens each chunk potential; α ∝1/K is the principled default.This tilt rule was not applied in the reported runs.Source: §C.6 · pp. 24–25
  • +0.100 at K = 6 and +0.121 at K = 8: boundary argmax exceeds pruning on the repetition reward summed over chunk pairs.At K = 8, the comparison covers 16 conditions; the interval for the +0.121 difference is [+0.060, +0.190].Source: Table 8 · p. 25, Table 9 · p. 26
  • At K = 6, beat-alignment boundary argmax trails pruning by 0.017 at α = 0.02 but leads by 0.026 at α = 0.01.At K = 8, boundary argmax at α = 0.01 leads pruning by 0.021.Source: Table 8 · p. 25, Table 9 · p. 26
  • The K = 8 music grid was not run because rolling-context clips failed the pre-set tempo-adherence gate, so the horizon results are dance-only.The K = 8 base clips had 0.85 tempo adherence against 0.95 at K = 4, a −10.5% relative change.Source: §C.6 · pp. 25–26

C.7 FULL RESULTS BY BUDGET, SCALE AND HELD-OUT QUANTITIES

The supplied tables document held-out quantities, paired intervals, and reward results across budgets, return rules, and model scales. Their captions specify the comparisons and scope but do not provide enough cell values here to report additional outcomes.

C.7 FULL RESULTS BY BUDGET, SCALE AND HELD-OUT QUANTITIES

  • At N = 32, Table 10 reports ranges of held-out quantities across steered methods against the base, including dance and music measures.The caption identifies beat-alignment steering for dance values and prompt-adherence steering for music values.Source: Table 10 · p. 27
  • Table 11 gives paired 95% bootstrap intervals over 40 conditions for N = 32 comparisons reported in Table 1 and Section 4.3.A dash marks a pair without a stored paired interval.Source: Table 11 · p. 27
  • Tables 12–15 organize reward results by particle count for beat alignment, repetition, prompt adherence and motif recurrence.The captions specify reward, model or return-rule scope and note budgets where argmax sequences were not regenerated.Source: Table 12 · p. 27, Table 13 · p. 28, Table 14 · p. 28
  • Table 16 compares N = 32 rewards on the 4M and 38M dance models under both return rules, including LatticeSMC argmax differences against pruning.The caption reports identical beat-alignment orderings at both model sizes.Source: Table 16 · p. 28

D HUMAN EVALUATION PROTOCOL

The human evaluation compared LatticeSMC with three alternatives on matched conditions and budgets, finding preference for LatticeSMC across both reward-targeted and overall-preference questions.

D HUMAN EVALUATION PROTOCOL

  • Each of 40 conditions per testbed paired LatticeSMC with the base model, best-of-N, and chunk pruning at the same budget, yielding 120 pairs per testbed.Within each pair, both sequences shared the condition and generation seed, and method identities were hidden.Source: D HUMAN EVALUATION PROTOCOL · p. 29
  • Sixty retained participants, 30 per testbed, provided five valid ratings per pair after attention-check exclusions.Each participant judged 20 substantive pairs in a session of about 40 minutes.Source: D HUMAN EVALUATION PROTOCOL · p. 29
  • Raters answered a reward-targeted question followed by an overall-preference question, while win rates counted no-preference responses as half.The reported intervals are 95% percentile bootstraps over the 40 conditions, without multiple-comparison adjustment.Source: D HUMAN EVALUATION PROTOCOL · p. 29
  • LatticeSMC exceeded 50% reward-question win rate in 26–34 of 40 dance conditions and 28–34 of 40 music conditions across the three comparators.Overall-preference counts were 26–28 of 40 for dance and 25–28 of 40 for music; Table 17 reports pairwise preference percentages with bootstrap intervals.Source: D HUMAN EVALUATION PROTOCOL · p. 29, Table 17 · p. 29
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