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Error-Corrected Inference-Time Scaling for Imperfect Diffusion Models

Zuokai Wen, Louis Grenioux, Weinan E, Jiequn Han

arXiv:2610.01933v1stat.MLcs.LG

TL;DR

Imperfect pretrained diffusion models can leave endpoint and path-tracking errors that more particles do not remove. EBFKC uses prescribed-path Feynman–Kac dynamics and progressive target-energy correction to address both errors. Across several benchmark systems, it recovers target distributions and molecular free-energy profiles where standard inference-time scaling baselines retain errors.

  • Problem

    Existing inference-time scaling methods assume exact pretrained models, although imperfect learned scores can produce endpoint and path-tracking errors that additional particles cannot remove.

    Source: §2.2 · p. 4

  • Method

    EBFKC tracks a prescribed path with Feynman–Kac dynamics approximated by SMC and progressively incorporates the reference-energy discrepancy to align the terminal target.

    Source: §1 · p. 2, §3.1 · p. 5, §3.2 · p. 6

  • Results

    Across Gaussian mixtures, particle systems, and alanine dipeptide and tetrapeptide, EBFKC on EAT corrects bias and recovers target distributions and molecular free-energy profiles where baselines fail.

    Source: §1 · p. 2, §5 · p. 10

  • Takeaways & Limitations

    Both path-tracking correction and endpoint correction are needed in the reported systems for EBFKC on EAT to recover targets under annealing and reward tilting and produce accurate molecular free-energy profiles.

    Source: §5 · p. 10

    The prescribed path must be normalizable, its initial distribution must be easy to sample, and its potential and required derivatives must be evaluable; its normalizer need not be known.

    Source: §3 · p. 4

Abstract

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Inference-time scaling adapts pretrained diffusion models to new sampling tasks without additional training. Existing methods rely primarily on Monte Carlo sampling with more particles, yet are premised on the pretrained model being exact. In practice, data and training limitations make the model imperfect, and these methods inherit its error. More particles reduce Monte Carlo error but cannot remove the mismatch between the endpoint and the desired target or the error in tracking the prescribed probability path. We introduce the Energy-based Feynman-Kac Corrector (EBFKC), a framework for energy-based diffusion models that corrects these errors on the fly given a reference energy. We first derive Feynman-Kac dynamics that track a prescribed path exactly in the continuous-time population limit even when the model is imperfect, and approximate these dynamics using sequential Monte Carlo with variance-controlling guidance. To remove the endpoint mismatch, we use the pretrained energy as a surrogate along the diffusion path and progressively incorporate the discrepancy between the learned and target terminal energies. Experiments on Gaussian mixture models, particle systems, alanine dipeptide, and alanine tetrapeptide show that our method closely matches target distributions and molecular free-energy profiles under annealing and reward tilting, whereas standard inference-time scaling baselines retain substantial sampling errors.

1 INTRODUCTION

Training separate diffusion models for new targets is costly, while existing inference-time scaling methods can inherit errors from imperfect pretrained models. EBFKC corrects path tracking and terminal mismatch using a prescribed-path Feynman–Kac flow and progressive target-energy correction; across several benchmarks, it recovers target distributions and molecular free-energy profiles where baselines fail.

Motivation

  • Training a separate diffusion model for each new target is often impractical, and imperfect pretrained scores can leave errors that adding particles cannot remove.Fine-tuning is also computationally expensive, motivating inference-time scaling.Source: §1 · pp. 1–2

Method

  • EBFKC derives Feynman–Kac dynamics for any prescribed path and uses sequential Monte Carlo with variance-controlling guidance to track it exactly at the population level despite model imperfection.This removes path-tracking error without assuming the pretrained model is exact.Source: §1 · p. 2
  • EBFKC on EAT uses the pretrained energy as a surrogate along the path and progressively incorporates the reference energy to remove endpoint mismatch.The reference energy pins the terminal distribution to the desired target.Source: §1 · p. 2

Results

  • Across Gaussian mixtures, particle systems, and two alanine systems, EBFKC on EAT corrects pretrained-model bias and recovers target distributions and molecular free-energy profiles where baselines fail.The benchmarks include annealing and reward tilting.Source: §1 · p. 2

2 BACKGROUND AND PROBLEM FORMULATION

The section sets up diffusion-based inference-time scaling and explains how energy-based densities support reweighting, while imperfect pretrained models introduce both endpoint and path-tracking errors. It distinguishes the model-induced target from the desired reference target and illustrates how the two errors affect particle trajectories.

2.1 SCORE- AND ENERGY-BASED DIFFUSION MODELS

  • The forward diffusion carries the data distribution to a tractable reference, and generation runs in reverse time from that reference toward the data distribution.The forward drift is taken to be linear, yielding closed-form Gaussian transition kernels.Source: §2.1 · p. 3
  • When the learned score only approximates the true score, the generated terminal law is only an approximation of the data distribution.The exact reverse diffusion matches the true marginals when the scores agree everywhere.Source: §2.1 · p. 3
  • An energy-based model defines explicit intermediate densities, unlike a directly parameterized score, and those densities support path reweighting and target alignment.Its score is the negative spatial gradient of the energy; the intermediate densities need not match the reverse-SDE law or the true marginals.Source: §2.1 · p. 3

2.2 INFERENCE-TIME SCALING WITH IMPERFECT MODELS

  • Inference-time scaling adapts a pretrained model to a new target by sampling from a path that uses the model’s densities as a tractable starting point.The reference energy specifies the target, while the pretrained densities are expected to provide a closer starting point than sampling from that energy directly.Source: §2.2 · p. 3
  • The model-induced target (MIT) interpolates through the pretrained model’s densities and ends at the model’s terminal energy, with an intermediate reward interpolating from zero to the desired reward.Its endpoint equals the desired target only when the reference energy matches the pretrained terminal energy.Source: §2.2 · pp. 3–4
  • Imperfect models create endpoint mismatch when the MIT differs from the reference target and path-tracking error when learned densities fail to satisfy the diffusion’s Fokker–Planck equation.Existing reweighting can then be biased and fail to track the intended path, even at the population level.Source: §2.2 · pp. 3–4
  • In the illustrated Gaussian-mixture example, only EBFKC on EAT reaches the desired target; FKC on EAT loses all but one lineage, while EBFKC on MIT retains endpoint mismatch.The figure contrasts four combinations of reweighting scheme and prescribed path.Source: Figure 1 · p. 4

3 METHOD

EBFKC separates the prescribed probability path from the pretrained model’s marginals, enabling exact population-level path tracking despite model error. EAT then corrects the terminal energy while retaining a flexible intermediate path.

3.1 FOKKER–PLANCK EQUATION FOR A PRESCRIBED PATH

  • SMC approximates the normalized Feynman–Kac flow with weighted particles and optional resampling, while VCG modifies drift to mitigate particle-weight degeneracy.Source: §3.1 · p. 5
  • EBFKC derives reweighting dynamics from a prescribed path potential, tracking sufficiently smooth, positive, normalizable paths exactly in the continuous-time population limit despite an imperfect model.Its state-dependent potential corrects the proposal/path discrepancy; centering preserves normalization and avoids needing ∂t log Zt.Source: §3.1 · p. 5

3.2 FROM MODEL-INDUCED TO ENERGY-ALIGNED TARGET

  • EAT changes only the terminal distribution, progressively adding the reference-versus-learned terminal-energy discrepancy while retaining the model-induced intermediate path.The correction vanishes when the reference energy equals the learned terminal energy and closes the mismatch when the reference is E⋆.Source: §3.2 · pp. 5–6

3.3 CONNECTIONS TO ANNEALED SMC AND ENERGY-BASED MODELING

  • Unlike geometric tempering, diffusion smoothing eases transport between modes; EBFKC generalizes reweighting to arbitrary reference energies without baking the terminal constraint into the architecture.Source: §3.3 · p. 6
  • Energy-based diffusion models provide path densities directly for reweighting, whereas score-based models require costly score integration that adds numerical error.Source: §3.3 · p. 6

4 EXPERIMENTS

Experiments test inference-time adaptation across controlled-error Gaussian mixtures, particle systems, and molecular annealing and free-energy tasks. Across the systems, only EBFKC on EAT recovers the reference, with added runtime relative to EBFKC on MIT.

4 EXPERIMENTS

  • Across all systems, only EBFKC on EAT recovers the reference; it takes approximately 1.1–3.6× the runtime of EBFKC on MIT.The reported runtime increase reflects additional energy and derivative evaluations; all methods use VCG unless marked otherwise.Source: §4 · p. 6

4.1 GAUSSIAN MIXTURE MODEL

  • EBFKC on EAT maintains low SWD as pretrained-model error increases in both GMM tasks, while EBFKC on MIT and FKC on EAT increasingly deviate from the reference.At the fixed error setting, EBFKC on EAT has the lowest mean error on all five reported metrics for both tasks.Source: §4.1 · p. 7, Figure 2 · p. 7

4.2 PARTICLE SYSTEMS

  • For Double-Well and Lennard-Jones systems, EBFKC on EAT matches reference distributions, unlike methods that retain pretrained-model error.For Lennard-Jones reward tilting, geometric-tempering SMC also fails to sample the target accurately at the same particle count.Source: §4.2 · p. 8, Figure 3 · p. 8

4.3 ALANINE DIPEPTIDE ANNEALING

  • In ALDP annealing from 800 K to 300 K, EBFKC on EAT recovers the reference conformational basins and relative populations, while EBFKC on MIT deviates substantially.FKC was numerically unstable on both paths in these runs; removing the look-ahead map also led to numerical instability.Source: §4.3 · p. 8, Figure 4 · p. 8, Table 2 · p. 9

4.4 FREE-ENERGY ESTIMATION

  • At 300 K, EBFKC on EAT reproduces ALDP’s umbrella-sampling barriers and basin structure and Ala-4’s OPES basin-and-barrier structure; EBFKC on MIT distorts both profiles.For Ala-4, EBFKC on EAT biases only ϕ3, whereas the OPES reference biases ϕ1, ϕ2, and ϕ3.Source: §4.4 · p. 9, Figure 5 · p. 9

5 CONCLUSION

The conclusion presents EBFKC as an inference-time framework for imperfect pretrained energy-based diffusion models, combining path tracking with terminal-energy correction. The authors report recovery of target distributions and molecular free-energy profiles, while identifying hand-designed schedules and derivative-evaluation costs as future work.

5 CONCLUSION

  • EBFKC combines population-level path tracking with SMC and VCG, then uses EAT to remove endpoint mismatch; across the evaluated systems, it recovers target distributions and accurate molecular free-energy profiles.The conclusion identifies extensions to discrete diffusion, automatic correction schedules, lower derivative-evaluation costs, and correction of larger pretrained equilibrium samplers as future directions.Source: §5 · pp. 9–10

AI USE STATEMENT

  • The authors report using generative AI to polish writing and assist with coding, and state that they reviewed the resulting work.They say they take responsibility for the final content, claims, and artifacts.Source: AI USE STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

  • The paper says its algorithmic specifications, proofs, experimental settings, and hyperparameters are provided, while code is to be released later.The authors describe these materials as intended to facilitate reproduction.Source: REPRODUCIBILITY STATEMENT · p. 10

A ENERGY-BASED DIFFUSION MODEL TRAINING

The appendix details energy-model training and the Feynman–Kac correction machinery, including variance control and look-ahead evaluation. It also describes derivative and stochastic trace-estimation procedures and their implementation constraints.

A ENERGY-BASED DIFFUSION MODEL TRAINING

  • Training uses denoising score matching in Stage 1 and optional noise-level classification in Stage 2 to calibrate relative proportions across disjoint energy regions.Stage 1 matches local energy properties; Stage 2 trains the model to identify the noise level of a perturbed sample.Source: A ENERGY-BASED DIFFUSION MODEL TRAINING · pp. 13–14

B.1 FOKKER–PLANCK EQUATION FOR A PRESCRIBED PATH

  • The prescribed-path derivation obtains a Feynman–Kac reweighting potential from the Fokker–Planck equation and normalizes it using an expectation under a vanishing-boundary-flux assumption.The normalization term is expressed as the expectation of the uncentered potential under q_t.Source: §B.1 · p. 15

B.2 VARIANCE-CONTROLLING GUIDANCE

  • Variance-Controlling Guidance adds a control drift and selects it to minimize residual-potential variance, with a regularized linear-basis solve for the control.For the EAT path, the active basis can include identity, learned-energy, target-energy-correction, and reward terms; the target-energy-correction basis is noted as important for control-drift estimation.Source: §B.2 · pp. 15–16

B.3 LOOK-AHEAD MAP

  • For challenging Lennard-Jones and molecular tasks, a look-ahead point interpolates between the current state and denoiser prediction to stabilize high-noise energy evaluations.Correction activates later in the reverse process; the schedules preserve the terminal potential while changing intermediate marginals.Source: §B.3 · p. 16

B.4 DERIVATIVE COMPUTATION AND STOCHASTIC LAPLACIAN ESTIMATION

  • For target-energy look-ahead terms, centered finite differences of the composite gradient approximate Hessian-vector products using only first-order target-energy derivatives.The text notes that the OpenMM finite-difference approximation is time-consuming and cannot be parallelized across particles.Source: §B.4 · p. 17
  • Stochastic Laplacian noise can bias normalized particle weights even when the estimated log-weight increment is conditionally unbiased, so the method subtracts half an estimated variance.The implementation applies this correction only to the Ala-4 free-energy experiment; other experiments showed no noticeable sampling-performance effect.Source: §B.4 · p. 18
  • Hutch++ is described as a low-rank-plus-residual trace estimator that can reduce residual variance when the sketch captures dominant Hessian components, but it is not used in the implementation.The authors leave Hutch++ for future work.Source: §B.4 · pp. 18–19

B.5 FKC WITH A TIME-DEPENDENT REWARD

This section describes Feynman–Kac correction for time-dependent rewards, including model-free SMC and a numerical-stability filter, alongside benchmark and molecular free-energy methods. It also outlines free-energy estimation from weighted samples and training and inference procedures for reward-corrected diffusion sampling.

B.5 FKC WITH A TIME-DEPENDENT REWARD

  • The time-dependent-reward extension generalizes Skreta et al. (2025, Proposition 3.4) and yields exact normalized weighted marginals when the base density satisfies the diffusion equation.It covers arbitrary deterministic rewards that are C1 in time and C2 in space, subject to integrability and vanishing-boundary-flux conditions.Source: §B.5 · p. 19
  • MIT uses reward Rt = rt, while EAT removes endpoint mismatch by construction; imperfect models can still cause path-tracking error when they violate diffusion consistency.EBFKC avoids this limitation by evaluating the full prescribed-path potential without requiring diffusion consistency.Source: §B.5 · pp. 19–20

B.6 TEMPERING MODEL-FREE SMC

  • The model-free baseline uses traditional SMC on a geometric tempering path, with annealed Langevin proposals, reward-based reweighting, and ESS-triggered resampling.The particle SDE uses drift vt = −εt∇Φt and diffusion coefficient σt = √2εt.Source: §B.6 · p. 20

B.7 ALIVE FILTER FOR NUMERICAL STABILITY

  • An energy-based alive filter prevents non-finite or extremely high-energy look-ahead configurations from propagating and destabilizing subsequent VCG and SMC reweighting.It replaces filtered particles using systematic resampling from surviving particles; in practice, it removes only a few particles without observed performance degradation.Source: §B.7 · pp. 20–21

C.1 GMM SETTINGS

  • The GMM benchmark uses 40 equally weighted components in 30 dimensions, with controlled mean and variance perturbations to model error under annealing and reward tilting.The primary comparisons set σµ = 10 and ρ = 0.1, and robustness sweeps vary each perturbation across five values.Source: §C.1 · pp. 21–22

C.2 PARTICLE SYSTEM SETTINGS

  • The particle-system settings test reward tilting on Double-Well DW-4 and Lennard-Jones LJ-13 systems, using quadratic rewards that increase effective confinement.Ground-truth reference samples come from underdamped Langevin simulations using BAOAB; the default reward strength is λ′ = 0.5.Source: §C.2 · p. 22

C.3 ALANINE DIPEPTIDE SETTINGS

  • For alanine dipeptide, supplied configurations include 210,384 at 300 K and 150,000 at 800 K; the 300 K free-energy profile along backbone dihedral ϕ is estimated using umbrella sampling.The reaction coordinate is computed from atom quadruplet (4, 6, 8, 14), using 25 umbrella windows uniformly spaced over its periodic domain.Source: §C.3 · p. 23

C.4 ALANINE TETRAPEPTIDE SETTINGS

  • The alanine tetrapeptide setup estimates the 300 K free-energy profile along ϕ3 using reference data from OPES-biased molecular dynamics across the three slow dihedrals.The benchmark uses unconstrained Cartesian coordinates; diffusion-based tilting methods share window definitions, sampling budgets, and angular bins.Source: §C.4 · pp. 23–24

C.5 MOLECULAR FREE-ENERGY ESTIMATION METHODS

  • Pooled particles are reweighted to estimate target-state observables; normalized equilibrium weights then estimate unbiased observables and free-energy profiles along ξ.The profile is constructed from the weighted marginal density along ξ, using probability-mass bins to form a PMF.Source: §C.5 · pp. 24–25

C.6 TRAINING AND INFERENCE DETAILS

  • Reward and target-correction schedules use independently configured activation and growth, with Ala-4 windows choosing reward-first or target-first order according to pretrained particle support.Both orders share terminal values αT = κT = 1; low-probability ϕ3 > 0 windows correct model error before concentrating particles in the window.Source: §C.6 · p. 26
  • Molecular SMC uses MALA rejuvenation, with its activation and step frequency varying by system and additional steps after resampling and at the endpoint.For Ala-4 umbrella sampling, MALA begins at SMC step 500, runs two steps every 10 steps, and adds five final steps; four steps follow each resampling event in molecular experiments.Source: §C.6 · pp. 26–27

C.7 EVALUATION METRICS

The evaluation compares generated and reference distributions using global sample, kernel, Wasserstein, structural, and energy-based metrics. Alanine dipeptide evaluation additionally assesses conformational basins, energy, and interatomic distances.

C.7 EVALUATION METRICS

  • GMM metrics include NLL difference, MMD, SWD, mean L2 distance, and Frobenius covariance distance between generated and reference samples.The GMM evaluation uses an RBF kernel for MMD and 10 uniformly sampled projection directions for SWD.Source: §C.7 · p. 27
  • Particle-system evaluation combines NLL difference, MMD, and SWD with metrics for interparticle structure and target-energy distributions.The reported structural and energy Wasserstein-1 distances compare pooled pairwise-distance and target-energy distributions, respectively.Source: §C.7 · p. 28
  • Alanine dipeptide evaluation uses Ramachandran TVD and basin-population error to compare backbone-angle distributions and four regions of the Ramachandran plane.Each run compares 25,000 generated samples with reference configurations at the corresponding temperature, after centering and chirality folding.Source: §C.7 · p. 28
  • Alanine dipeptide energy TVD and distance TVD compare binned reduced-energy and pooled atomic-distance distributions against reference ranges.The energy evaluation excludes samples outside the reference energy range before normalizing histograms.Source: §C.7 · p. 28

D.1 GMM RESULTS

On the GMM, FKC on EAT without variance-controlling guidance misses target modes, and substantial sampling error remains even at zero pretrained-model error. EAT variants also take longer than MIT variants.

D.1 GMM RESULTS

  • FKC on EAT and EBFKC on EAT take longer than either MIT variant because EAT requires additional target-energy evaluations.Table 5 reports runtime for the 30-dimensional GMM under σµ = 10 and ρ = 0.1, with means and standard deviations over five runs.Source: §D.1 · p. 29, Table 5 · p. 29
  • Without VCG, FKC on EAT misses target modes under both annealing and reward tilting, and the SWD sweep shows substantial error even at zero pretrained-model error.The SWD error has no monotonic dependence on pretrained-model perturbation; together, these findings support VCG’s role in stabilizing Feynman–Kac dynamics.Source: §D.1 · pp. 28–29, Figure 6 · p. 29, Figure 7 · p. 29

D.2 DOUBLE-WELL RESULTS

On the double-well system, EBFKC on EAT closely matches target RDF and energy distributions under annealing and reward tilting, while FKC on EAT and EBFKC on MIT retain substantial deviations. On DW-4, EBFKC on EAT takes 11% longer than EBFKC on MIT in both tasks.

D.2 DOUBLE-WELL RESULTS

  • 11% longer runtime for EBFKC on EAT than EBFKC on MIT on both DW-4 tasks, with target-energy second derivatives evaluated directly rather than by finite differences.Table 6 reports mean runtime and standard deviation over five runs.Source: §D.2 · p. 30, Table 6 · p. 30
  • EBFKC on EAT closely matches the target RDF and energy distributions in both tasks, whereas FKC on EAT and EBFKC on MIT retain substantial deviations.The pretrained model’s reverse-diffusion samples also miss reference RDF peaks and shift toward higher energies.Source: Figure 9 · p. 30, §D.2 · p. 30, Figure 8 · p. 30

D.3 LENNARD–JONES RESULTS

For LJ-13 annealing, EBFKC on EAT closely reproduces the reference distributions, while EBFKC on MIT and tempering SMC retain errors. The section also reports runtime comparisons and shows the scope of the particle-system benchmarks.

D.3 LENNARD–JONES RESULTS

  • Figures 10 and 11 compare reference distributions with FKC and EBFKC variants for double-well reward tilting and Lennard–Jones annealing, respectively.Source: Figure 10 · p. 31, Figure 11 · p. 31
  • EBFKC on EAT closely reproduces the LJ-13 reference RDF peaks and energy distribution, while EBFKC on MIT deviates and tempering SMC shifts energy toward higher values.Table 7 summarizes five performance metrics on DW-4 and LJ-13 under annealing and reward tilting, but the supplied passage gives no metric values.Source: §D.3 · p. 31, Table 7 · p. 31
  • Finite-difference second-order derivatives make EBFKC on EAT slower than EBFKC on MIT with or without VCG on LJ-13.The required evaluations can be parallelized across particles; Table 8 reports runtime comparisons over five runs.Source: §D.3 · p. 32, Table 8 · p. 32

D.4 ALDP ANNEALING RESULTS

During ALDP annealing from 800 K to 300 K, EBFKC on EAT closely matches the reference marginals, unlike both MIT variants. The section also reports a runtime cost for target-energy correction and failures when the look-ahead map is removed.

D.4 ALDP ANNEALING RESULTS

  • At 300 K, EBFKC on EAT closely matches the reference marginals of both backbone dihedrals, while both MIT variants miss the leftmost major ϕ peak and overconcentrate the dominant positive-ψ peak.The pretrained model already shows visible discrepancies from the reference at 800 K.Source: §D.4 · p. 32, Figure 12 · p. 32, Figure 13 · p. 33
  • Finite-difference second-order target-energy derivatives require additional, non-parallelizable OpenMM evaluations, making EBFKC on EAT slower than EBFKC on MIT variants for 1,000-particle ALDP annealing.Table 9 reports runtime comparisons for annealing from 800 K to 300 K over five runs.Source: §D.4 · p. 32, Table 9 · p. 32
  • Without the look-ahead map, alive filtering permits all 1,000 annealing transitions but the endpoint check rejects every particle; without filtering, all 1,000 VCG potentials become non-finite at transition 816.The failure without filtering occurs when target-energy correction activates and target energy is evaluated at noisy particle states; alive filtering cannot fix this systematic failure.Source: §D.4 · pp. 32–33

D.5 MOLECULAR FREE-ENERGY ESTIMATION RESULTS

The pretrained ALDP and Ala-4 models capture broad features of the 300 K reference marginals but retain discrepancies. In free-energy estimation, EBFKC without VCG has substantial errors, while target-energy correction adds runtime overhead, with a smaller relative overhead for Ala-4 than ALDP.

D.5 MOLECULAR FREE-ENERGY ESTIMATION RESULTS

  • At 300 K, pretrained ALDP marginals capture broad reference shapes but miss some details, while pretrained Ala-4 marginals closely reproduce them with remaining discrepancies.Figures 14 and 15 compare the pretrained reverse-diffusion marginals with the reference distributions.Source: §D.5 · p. 33, Figure 14 · p. 33, Figure 15 · p. 34
  • Without VCG, EBFKC on MIT has large, variable ALDP free-energy errors and misses the positive-ϕ reference basin, while substantially underestimating Ala-4's positive-ϕ3 barrier.The ALDP comparison with EBFKC on MIT in Fig. 5(a) highlights the benefit of VCG; Fig. 16 shows the estimates against the stated references over five runs.Source: §D.5 · pp. 33–34, Figure 16 · p. 35
  • Finite-difference second-order target-energy derivatives add non-parallelizable OpenMM evaluations, making EBFKC on EAT slower than MIT variants for ALDP free-energy estimation.For Ala-4, target-energy correction contributes a smaller relative runtime overhead because the larger pretrained model makes each baseline step more expensive; Tables 10 and 11 report runtimes over five runs.Source: §D.5 · p. 34, Table 10 · p. 35, Table 11 · p. 35

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