Pith. sign in

REVIEW 3 major objections 5 minor 51 references

FlowLOB: Efficient and Controllable Limit Order Book Generation with Flow Matching

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Flow matching can generate realistic limit order book trajectories at 10 ODE-solver steps, with better marginal realism than diffusion and four baselines at high frequencies.

desk verdict A solid, honest first flow-matching LOB generator; the efficiency claim is real within the tested solver family, but thinner once specialized diffusion samplers are added. read the letter →

arxiv 2608.13096 v1 pith:UAJKFNYU submitted 2026-08-13 cs.LG cs.CEq-fin.CPq-fin.TR

Zhuohan Wang , Andreea Bacalum , Ollie Olby , Carmine Ventre , Namid Stillman This is my paper · ORCID
classification cs.LGcs.CEq-fin.CPq-fin.TR
keywords flowmatchinglimitorderbooksgenerativemodelsdiffusionmarketsimulationcontrollablegenerationzero-shottransfersamplingefficiency
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

FlowLOB is built on a single claim: flow matching can generate realistic limit order book trajectories at a fraction of the sampling cost of diffusion, without sacrificing fidelity or the ability to steer scenarios. The paper trains flow and diffusion models with identical data, architecture, and budget, and samples both through the same fixed-step ODE solvers; flow matching reaches its best quality with 10 Euler steps, while diffusion needs many more function evaluations. At that cheap operating point, the distributions of generated prices and volumes are closer to real Hong Kong Exchange data than those from two learned and two agent-based simulators in most comparisons at the 0.1-second and 1-second frequencies, including on a symbol never seen in training. The conditioning variables also pass a distributional counterfactual test: swapping a scenario value for a tail value moves the generated statistic toward the corresponding real tail regime in 42 of 48 settings. If these results hold, practitioners get a simulator that is cheap enough to roll out at scale, generalizes to new instruments without retraining, and can be steered into rare regimes.

What carries the argument

The load-bearing object is the flow-matching velocity field learned along a straight-line interpolation path. For noise $z \sim \mathcal{N}(0,I)$ and data $x_0$, the interpolation is $x_t=(1-t)z+t x_0$ and the target velocity is the constant $x_0-z$; the network $v_\theta(x_t,c,t)$ is trained to regress that target, and sampling integrates the ODE $\frac{dx_t}{dt}=v_\theta(x_t,c,t)$ from $t=0$ to $t=1$ with conditioning $c$ held fixed. Because this path is nearly straight, coarse Euler integration already tracks it, which is why 10 function evaluations suffice. The supporting machinery is the tick-relative LOB representation—mid-price changes and level gaps measured in ticks (minimum price increments), volumes as $\log(V+1)$—which strips instrument-specific scale so one model can train across eight HKEX symbols and transfer to a ninth, and the adaLN-Zero transformer that treats each level–time cell as a token and aligns scenario conditioning channels with the corresponding future time steps.

What would settle it

Run the matched diffusion checkpoint with an accelerated sampler such as DDIM or DPM-Solver at 10 to 20 function evaluations and compare Wasserstein-1 distance to FlowLOB's Euler-10 output on the same test windows; if diffusion matches or beats FlowLOB at comparable NFE, the paper's central efficiency claim fails. A second check: re-run the 10s realism comparison with more training symbols or a longer history; if the flow model's marginals still trail zero-intelligence baselines, the stated boundary at coarse frequency is confirmed rather than a training-size artifact.

Watch

Extended reading notes

Core claim

Under a matched comparison in which flow matching and diffusion share the same dataset, transformer backbone, training recipe, and family of fixed-step ODE solvers, flow matching reaches its best sample quality with only 10 Euler steps, while the diffusion baseline needs many more function evaluations to approach the same fidelity; at equal sampling cost the flow model's marginal distributional error is 4 to 120 times lower across price and volume features. Using Euler with 10 steps as the default operating point, FlowLOB beats LOB-S5, LOB-GAN, Hawkes, and zero-intelligence baselines in 30 of 32 price/volume metric cells at 0.1s and 1s, on both an in-distribution symbol and a held-out symbol, with a median 4.5 times smaller distance than the best non-flow baseline. The counterfactual test replaces one scenario variable with a high or low 5% tail value and asks whether the generated statistic moves toward the corresponding real tail regime; this succeeds in 42 of 48 cases, with liquidity and imbalance reliably steerable at every frequency. The paper further shows zero-shot transfer to a ninth symbol and that the transformer backbone matters most out of distribution, while noting that at the coarsest 10s frequency the realism advantage mostly disappears.

Load-bearing premise

The load-bearing premise is that measuring diffusion's sampling cost with the same generic fixed-step ODE solvers used for flow matching is a fair comparison; the paper deliberately excludes the accelerated diffusion samplers it cites, so if those close the function-evaluation gap, the claimed 4 to 120 times efficiency advantage would shrink or disappear.

Editorial extensions

If this is right

  • At a fixed compute budget, a generator that is accurate after 10 network evaluations can produce many more simulated days, symbols, and random seeds than one requiring tens or hundreds of evaluations, changing what is feasible for stress testing and reinforcement-learning training.
  • Because one model covers multiple symbols through the tick-relative representation, a new instrument can be simulated zero-shot, without per-symbol retraining or new calibration data.
  • Conditioning on liquidity and imbalance reliably shifts generated books into the requested tail regime, so the same generator can be used to produce counterfactual scenarios for what-if analysis.
  • At 0.1s and 1s, FlowLOB's pooled price and volume marginals are closer to real data than the four baselines on nearly all metrics, while at 10s the advantage weakens, limiting the method's use at coarser resolutions in its current form.
  • Because flow and diffusion were trained with identical data, backbone, and budget and sampled with the same solvers, the measured quality-cost gap reflects the generative dynamics themselves rather than a difference in architecture or training setup.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The efficiency comparison is a lower bound on diffusion's speed only if specialized samplers such as DDIM and DPM-Solver, which the paper cites but does not run, are excluded; testing FlowLOB's Euler-10 checkpoint against diffusion with those samplers at equal NFE would settle whether the 4 to 120 times gap is intrinsic or an artifact of the solver family.
  • The tick-relative representation is likely to transfer to other exchanges and asset classes with different tick sizes and price scales, since it removes instrument-specific units; this is a testable extension rather than something the paper demonstrates.
  • The counterfactual test changes one condition at a time; a natural extension is joint control, such as high volatility and low liquidity together, or control over derived statistics such as return tails, which the paper does not attempt.
  • Flow matching's near-straight paths could make the model amenable to consistency-style distillation for even fewer evaluations, but the paper does not explore that; it would be a separate speedup on top of the 10-step operating point.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper introduces FlowLOB, a conditional flow-matching model that generates limit order book trajectory windows (twenty price levels, thirty-two future steps) from a transformer backbone conditioned on trend, volatility, liquidity, and imbalance, trained jointly on eight HKEX symbols at 0.1s, 1s, and 10s resolutions using a tick-relative representation. The central claims are: (i) flow matching reaches its best quality at 10 Euler steps, giving a 4-120x lower marginal distributional error than an equally trained diffusion model sampled with the same fixed-step ODE solvers; (ii) at this operating point FlowLOB is more realistic than LOB-S5, LOB-GAN, Hawkes, and zero-intelligence baselines in 30 of 32 cells at 0.1s and 1s, including zero-shot transfer to a held-out symbol; and (iii) replacing conditioning values with high- or low-tail values moves generated books toward the corresponding real tail regime in 42 of 48 counterfactual cells. The paper honestly reports that the realism advantage weakens at 10s and that trend control is less reliable, and it concludes with a stated plan to study scaling behavior.

Significance. If the claims hold, the paper makes a practically useful contribution: a single multi-symbol, zero-shot-transferable LOB generator with a low-NFE sampling operating point and a distributional test of counterfactual validity is exactly what practitioners need for large-scale rollout simulation. The matched flow-versus-diffusion setup, with identical data, architecture, optimizer, and solver family, is a strength, as is the tick-relative preprocessing that enables cross-symbol generalization. The controllability criterion, which measures whether the generated statistic actually moves toward the requested real tail regime, is a meaningful improvement over mere conditioning. The disclosed 10s limitation and the clear statement of the operating point chosen for downstream experiments are also positive signs of methodological honesty. The main weakness is that the headline efficiency result is scoped to a single family of fixed-step solvers and lacks the specialized diffusion samplers the paper itself cites; the evaluation also lacks error bars or significance tests, so several 'best in 30 of 32 cells' claims rest on a single run.

major comments (3)
  1. [§4.2, §3.2] The headline efficiency claim rests on a sampling protocol that excludes the specialized diffusion samplers cited in §2 (DDIM, DPM-Solver, UniPC). The statement in §4.2 that 'at the same sampling compute, its marginal distributional error is 4–120× lower than diffusion' is not yet supported as a practical efficiency claim, because those samplers are specifically designed to integrate the probability-flow ODE at 10–20 NFE and could close much of the gap. The paper dismisses such samplers in the Introduction as 'treating the symptom rather than the problem,' but this is a conceptual argument, not an empirical one; for a practitioner comparing models, a 10-step DPM-Solver that reaches FlowLOB's fidelity would erase the practical advantage. Please include at least one of these samplers (or a comparable accelerated diffusion sampler) in the NFE sweep, or explicitly state and justify why they cannot be applied to the chosen noise schedule and probability-flow ODE.
  2. [§3.1, §3.2] The diffusion baseline is not fully specified, which makes the controlled comparison impossible to reproduce independently. In §3.1 the variance-preserving noising path is written as x_t = α_t x_0 + σ_t ε, but the actual schedule (α_t, σ_t) is never given, and in §3.2 the conversion from the noise prediction to the probability-flow ODE field is described only verbally ('converted into the corresponding probability-flow ODE field'). Please provide the explicit schedule, the exact ODE field, and the integration limits used for the diffusion sampler, so that the fairness of the solver comparison and the reproducibility of the 4–120× ratio can be assessed.
  3. [§4.1, §4.3, Table 1 and Table 2] All realism and controllability claims are based on a single trained checkpoint and a single evaluation pass. Table 1 reports distances without error bars or significance tests, Table 2 contains rounded ties marked with asterisks, and Figure 3 shows no variance information. The claim in §4.5 that the conclusions are 'not artifacts of a lucky training setting' cannot be supported without multiple seeds or bootstrap confidence intervals over the evaluation data. Please add at least seed-variation or bootstrapped intervals for the key comparisons in Tables 1 and 2 and for the NFE curves in Figure 1; otherwise the 30-of-32 and 42-of-48 headline numbers may overstate the robustness of the differences.
minor comments (5)
  1. [§1, §4.2] The abstract states that 'flow matching attains its best quality with only 10 ODE-solver steps,' while §4.2 reports that Flow-Euler-10 is the best point in only four of six panels and uses 'best or nearly best' elsewhere; please align the wording with the figure.
  2. [§4.3, Table 1] The volume W1 values in Table 1 are orders of magnitude larger than the price W1 values; please state explicitly whether the distances are computed on the log-transformed volume representation introduced in §3.3 or on the raw volume scale, and what units the reported numbers have.
  3. [§4.1] The adaptation of the ZI and Hawkes baselines from Kawawa-Beaudan et al. is described only as 'calibration procedures'; please specify the fitted marginal distributions, the Hawkes kernel family, and how the event streams are converted to the fixed-grid LOB representation used for evaluation.
  4. [§4.4] The counterfactual test in §4.4 does not report the number of past windows used for the reference and counterfactual samples, nor the size of the 5% tail sets; adding these details is needed to assess the statistical meaning of the 42-of-48 result.
  5. [Figure 2] The bottom-row cross-level correlation matrices are dense and difficult to read at print size; consider enlarging each panel or reporting the correlation differences numerically in a supplementary table.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: all central claims are empirical comparisons against held-out data and external baselines, with no fitted parameter renamed as a prediction and no load-bearing self-citation chain.

full rationale

The paper's derivation chain is not circular. FlowLOB's central claims are empirical: flow matching and diffusion are trained with identical data, architecture, and budget, and sampled through the same fixed-step ODE solvers; the reported 4-120x efficiency advantage is a measured outcome of that controlled comparison, not something forced by construction. The realism evaluation compares generated pooled marginals against real data and external learned and agent-based baselines, including a held-out symbol, so the results are externally anchored. The counterfactual controllability test defines validity as the counterfactual Wasserstein distance to the real tail regime being smaller than the reference distance, and then measures exactly that quantity; this is a legitimate behavioral criterion rather than a self-fulfilling definition, and the paper itself notes that the liquidity and imbalance channels are closely aligned with the output tensor. The self-citations to DiffLOB and DiffVolume are contextual and not load-bearing: no uniqueness theorem, no ansatz, and no fitted value is imported from those papers to make the current claims true. The efficiency comparison omits specialized diffusion samplers such as DDIM and DPM-Solver, but that is a scope limitation regarding the breadth of the efficiency conclusion, not circularity, and under the stated rules it does not raise the circularity score. The paper is self-contained against external benchmarks, so the honest finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new entities. Its free parameters are mostly standard training hyperparameters and the selected N=10 operating point. The domain assumptions are the main load-bearing items: the tick-relative representation, the conditioning-channel sufficiency, and the representativeness of one held-out symbol.

free parameters (4)
  • ODE solver steps N = 10
    Selected as the operating point from the quality-cost sweep in Sec 4.2; all downstream realism and controllability claims use this setting.
  • Conditioning dropout rate = 0.5
    Chosen in training recipe (Sec 4.1) for classifier-free guidance.
  • Learning rate = 1e-4
    Default rate; ablations at 5e-4 and 5e-5 (Sec 4.5).
  • Transformer parameter count = ~100M
    Reported only as ~100M configuration; exact dimensions not disclosed, so exact replication is impossible.
assumptions (6)
  • standard math Flow matching and diffusion objectives as defined in Sec 3.1 are valid conditional generative objectives.
    Based on established literature [27, 28, 15, 40]; the paper does not re-derive but builds on these.
  • standard math Deterministic probability-flow ODE integration is a valid way to sample both models.
    Sec 3.2 assumes the learned fields can be integrated by fixed-step solvers.
  • domain assumption Tick-relative price and log-volume representation removes enough instrument-specific scale to support pooled training and zero-shot transfer.
    Sec 3.3 asserts this 'key reason' for transfer, but no ablation varies the representation.
  • domain assumption The four conditioning channels (trend, volatility, liquidity, imbalance) are sufficient to describe desired market regimes.
    Sec 3.3 defines these channels; the controllability test in Sec 4.4 only measures these same statistics.
  • domain assumption The held-out symbol 9999.HK is representative of unseen instruments.
    Zero-shot transfer is evaluated on this single symbol over one month (Sec 4.1).
  • domain assumption Pooled marginal distances on price and volume are meaningful measures of LOB realism.
    Tables 1 and 2 evaluate marginal distributions; full pathwise dynamics are not scored.

how reviews work

0 comments
Cite this review

Pith. "Pith review of FlowLOB: Efficient and Controllable Limit Order Book Generation with Flow Matching." pith.science (2026). https://pith.science/paper/UAJKFNYU

@misc{pith2026260813096,
  author       = {Pith},
  title        = {Pith review of: FlowLOB: Efficient and Controllable Limit Order Book Generation with Flow Matching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UAJKFNYU}},
  note         = {Machine review of arXiv:2608.13096}
}
abstract

Limit order book (LOB) simulators are most useful to practitioners when they combine realistic market dynamics, computationally efficient sampling, controllable scenario generation, and the ability to generalize beyond the instruments seen during training---properties that existing agent-based and deep generative simulators provide only partially. We present \textbf{FlowLOB}, a conditional \textbf{flow}-matching generator of \textbf{LOB} trajectories, trained on multiple Hong Kong Exchange (HKEX) symbols at three sampling frequencies ($0.1$s, $1$s, $10$s) in tick-relative representation that transfers to unseen instruments. Because flow and diffusion models admit a common formulation, we train both with identical data, architecture, and budget, and sample both through the same fixed-step ODE solvers, yielding a controlled comparison of sampling efficiency and fidelity. Flow matching attains its best quality with only $10$ ODE-solver steps, whereas diffusion needs many more function evaluations to approach the same fidelity. At this efficient operating point, FlowLOB improves realism over baselines, two learned and two agent-based models, in most distributional metrics at the two finer sampling frequencies. We evaluate counterfactual controllability with a distributional test that asks whether changing a scenario condition moves the generated statistic toward the corresponding real tail regime; FlowLOB satisfies this criterion in most tested settings. Both realism and control effects transfer zero-shot on a held-out symbol. We additionally conduct ablation studies on the network architecture and the learning rate.

Figures

Figures reproduced from arXiv: 2608.13096 by the authors.

Figure 1
Figure 1. Sample quality versus inference cost. 𝑊1 distance to the real pooled price (left) and volume (right) marginals at the three sam￾pling frequencies (rows), against NFE on a log–log scale. Solid: flow matching; dashed: diffusion; one curve per solver; the star marks the best point per panel. Flow with Euler at 𝑁 =10 — the cheapest configuration in the sweep — is the best point in four of six panels. simple empirical ma… view at source ↗
Figure 2
Figure 2. Realism diagnostics beyond pooled marginals. Top subplot is about Mid-price return and bid–ask spread distributions. Bottom subplot [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Ablation results at 1s. We compare the proposed transformer configuration against a parameter-matched UNet and two learning-rate variants. Bars show distances between generated and real pooled price and volume marginals for the in-distribution symbol 700.HK and the held-out symbol 9999.HK; lower is better. ablation is not intended to exhaust the architecture space; rather, it tests whether the proposed configuration… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 17 canonical work pages

  1. [1]

    Albergo, Nicholas M

    Michael S. Albergo, Nicholas M. Boffi, and Eric Vanden-Eijnden. 2023. Stochastic Interpolants: A Unifying Framework for Flows and Diffusions.arXiv preprint arXiv:2303.08797(2023)

    arXiv 2023

  2. [2]

    Alfred Backhouse, Kang Li, Jakob Foerster, Anisoara Calinescu, and Stefan Zohren. 2025. Painting the Market: Generative Diffusion Models for Financial Limit Order Book Simulation and Forecasting.arXiv preprint arXiv:2509.05107 (2025)

    work page Pith review arXiv 2025

  3. [3]

    Emmanuel Bacry, Iacopo Mastromatteo, and Jean-François Muzy. 2015. Hawkes Processes in Finance.Market Microstructure and Liquidity1, 1 (2015), 1550005. 7 Wang et al

    work page 2015

  4. [4]

    Leonardo Berti, Bardh Prenkaj, and Paola Velardi. 2025. TRADES: Generating Re- alistic Market Simulations with Diffusion Models.arXiv preprint arXiv:2502.07071 (2025)

    arXiv 2025

  5. [5]

    Hans Bühler, Lukas Gonon, Josef Teichmann, and Ben Wood. 2019. Deep Hedging. Quantitative Finance19, 8 (2019). arXiv:1802.03042

    arXiv 2019

  6. [6]

    David Byrd, Maria Hybinette, and Tucker Hybinette Balch. 2020. ABIDES: Towards High-Fidelity Multi-Agent Market Simulation. InProceedings of the 2020 ACM SIGSIM Conference on Principles of Advanced Discrete Simulation. 11–22

    work page 2020

  7. [7]

    Andrea Coletta, Aymeric Moulin, Svitlana Vyetrenko, and Tucker Balch. 2022. Learning to Simulate Realistic Limit Order Book Markets from Data as a World Agent. InProceedings of the 3rd ACM International Conference on AI in Finance. 428–436

    work page 2022

  8. [8]

    Andrea Coletta, Matteo Prata, Michele Conti, Emanuele Mercanti, Novella Bartolini, Aymeric Moulin, Svitlana Vyetrenko, and Tucker Balch. 2021. To- wards Realistic Market Simulations: A Generative Adversarial Networks Ap- proach. InProceedings of the 2nd ACM International Conference on AI in Finance. arXiv:2110.13287

    work page Pith review arXiv 2021

Show all 51 references
  1. [9]

    Rama Cont. 2001. Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues.Quantitative Finance1, 2 (2001), 223–236

    2001

  2. [10]

    Prafulla Dhariwal and Alexander Quinn Nichol. 2021. Diffusion Models Beat GANs on Image Synthesis. InAdvances in Neural Information Processing Systems, Vol. 34. 8780–8794. arXiv:2105.05233

    2021 arXiv

  3. [11]

    Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas Müller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, Dustin Podell, Tim Dockhorn, Zion English, Kyle Lacey, Alex Goodwin, Yannik Marek, and Robin Rombach. 2024. Scaling Rectified Flow ...

    2024 arXiv

  4. [12]

    Doyne Farmer, Paolo Patelli, and Ilija I

    J. Doyne Farmer, Paolo Patelli, and Ilija I. Zovko. 2005. The Predictive Power of Zero Intelligence in Financial Markets.Proceedings of the National Academy of Sciences102, 6 (2005), 2254–2259

    2005

  5. [13]

    Gode and Shyam Sunder

    Dhananjay K. Gode and Shyam Sunder. 1993. Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality.Journal of Political Economy101, 1 (1993), 119–137

    1993

  6. [14]

    Panjing He, Mingyue Cheng, Li Li, and XiaoHan Zhang. 2025. TimeFlow: To- wards Stochastic-Aware and Efficient Time Series Generation via Flow Matching Modeling.arXiv preprint arXiv:2511.07968(2025)

    2025

  7. [15]

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. 2020. Denoising Diffusion Probabilistic Models. InAdvances in Neural Information Processing Systems, Vol. 33. 6840–6851. arXiv:2006.11239

    2020 arXiv

  8. [16]

    Jonathan Ho and Tim Salimans. 2022. Classifier-Free Diffusion Guidance. In NeurIPS Workshop on Deep Generative Models. arXiv:2207.12598

    2022 arXiv

  9. [17]

    Peter Holderrieth and Ezra Erives. 2026. An Introduction to Flow Matching and Diffusion Models.arXiv preprint arXiv:2506.02070(2026)

    2026

  10. [18]

    Li, Sheng Wang, Jiheng Zhang, Ziyun Li, and Tianlong Chen

    Yang Hu, Xiao Wang, Zezhen Ding, Lirong Wu, Huatian Zhang, Stan Z. Li, Sheng Wang, Jiheng Zhang, Ziyun Li, and Tianlong Chen. 2024. FlowTS: Time Series Generation via Rectified Flow.arXiv preprint arXiv:2411.07506(2024)

    2024 arXiv

  11. [19]

    Yu-Hao Huang, Chang Xu, Yang Liu, Weiqing Liu, Wu-Jun Li, and Jiang Bian. 2026. Controllable Financial Market Generation with Diffusion Guided Meta Agent. In Proceedings of the AAAI Conference on Artificial Intelligence. arXiv:2408.12991

    2026

  12. [20]

    Hanna Hultin, Henrik Hult, Alexandre Proutiere, Samuel Samama, and Ala Tarighati. 2023. A Generative Model of a Limit Order Book Using Recurrent Neural Networks.Quantitative Finance23, 6 (2023), 931–958

    2023

  13. [21]

    Konark Jain, Nick Firoozye, Jonathan Kochems, and Philip Treleaven. 2024. Limit Order Book dynamics and order size modelling using Compound Hawkes Process. Finance Research Letters69 (2024), 106157

    2024

  14. [22]

    Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. 2022. Elucidating the Design Space of Diffusion-Based Generative Models. InAdvances in Neural Information Processing Systems, Vol. 35. 26565–26577. arXiv:2206.00364

    2022 arXiv

  15. [23]

    Maxime Kawawa-Beaudan, Srijan Sood, Kassiani Papasotiriou, Daniel Borrajo, and Manuela Veloso. 2026. TradeFM: A generative foundation model for trade- flow and market microstructure.arXiv preprint arXiv:2602.23784(2026)

    2026

  16. [24]

    Junyi Li, Xintong Wang, Yaoyang Lin, Arunesh Sinha, and Michael P. Wellman

  17. [25]

    Yang Li and Zhi Chen. 2025. ByteGen: A Tokenizer-Free Generative Model for Orderbook Events in Byte Space.arXiv preprint arXiv:2508.02247(2025)

    2025 arXiv

  18. [26]

    Yang Li, Zhi Chen, and Steve Yang. 2025. FlowHFT: Imitation Learning via Flow Matching Policy for Optimal High-Frequency Trading under Diverse Market Conditions.arXiv preprint arXiv:2505.05784(2025)

    2025 arXiv

  19. [27]

    Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. 2023. Flow Matching for Generative Modeling. InInternational Conference on Learning Representations. arXiv:2210.02747

    2023 arXiv

  20. [28]

    Xingchao Liu, Chengyue Gong, and Qiang Liu. 2023. Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow. InInternational Conference on Learning Representations. arXiv:2209.03003

    2023 arXiv

  21. [29]

    Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu

  22. [30]

    Peer Nagy, Sascha Frey, Silvia Sapora, Kang Li, Anisoara Calinescu, Stefan Zohren, and Jakob Foerster. 2023. Generative AI for End-to-End Limit Order Book Modelling: A Token-Level Autoregressive Generative Model of Message Flow Using a Deep State Space Network. InProceedings o...

    2023 arXiv

  23. [31]

    Yuqi Nie, John M Mulvey, H Vincent Poor, Chenyu Yu, and Hao Huang. 2026. Deep generative models meet statistical methods: a generalized framework for financial regime identification.Annals of Operations Research(2026), 1–28

    2026

  24. [32]

    Ollie Olby, Andreea Bacalum, Rory Baggott, and Namid Stillman. 2025. Right Place, Right Time: Market Simulation-based RL for Execution Optimisation. In Proceedings of the 6th ACM International Conference on AI in Finance. 898–905

    2025

  25. [33]

    William Peebles and Saining Xie. 2023. Scalable Diffusion Models with Trans- formers. InProceedings of the IEEE/CVF International Conference on Computer Vision. arXiv:2212.09748

    2023 arXiv

  26. [34]

    Ethan Perez, Florian Strub, Harm De Vries, Vincent Dumoulin, and Aaron Courville. 2018. Film: Visual reasoning with a general conditioning layer. In Proceedings of the AAAI conference on artificial intelligence, Vol. 32

    2018

  27. [35]

    Vamsi K Potluru, Daniel Borrajo, Andrea Coletta, Niccolò Dalmasso, Yousef El-Laham, Elizabeth Fons, Mohsen Ghassemi, Sriram Gopalakrishnan, Vikesh Gosai, Eleonora Kreačić, et al. 2023. Synthetic data applications in finance.arXiv preprint arXiv:2401.00081(2023)

    2023 arXiv

  28. [36]

    Weiss, Niru Maheswaranathan, and Surya Ganguli

    Jascha Sohl-Dickstein, Eric A. Weiss, Niru Maheswaranathan, and Surya Ganguli

  29. [37]

    Jiaming Song, Chenlin Meng, and Stefano Ermon. 2021. Denoising Diffu- sion Implicit Models. InInternational Conference on Learning Representations. arXiv:2010.02502

    2021 arXiv

  30. [38]

    Yang Song, Prafulla Dhariwal, Mark Chen, and Ilya Sutskever. 2023. Consistency Models. InProceedings of the 40th International Conference on Machine Learning. arXiv:2303.01469

    2023 arXiv

  31. [39]

    Yang Song and Stefano Ermon. 2019. Generative Modeling by Estimating Gra- dients of the Data Distribution. InAdvances in Neural Information Processing Systems, Vol. 32. arXiv:1907.05600

    2019 arXiv

  32. [40]

    Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole

    Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. 2021. Score-Based Generative Modeling through Stochas- tic Differential Equations. InInternational Conference on Learning Representations. arXiv:2011.13456

    2021 arXiv

  33. [41]

    Yuki Tanaka, Ryuji Hashimoto, Takehiro Takayanagi, Zhe Piao, Yuri Murayama, and Kiyoshi Izumi. 2025. CoFinDiff: Controllable Financial Diffusion Model for Time Series Generation. InProceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence. 9357...

    2025 arXiv

  34. [42]

    Svitlana Vyetrenko, David Byrd, Nick Petosa, Mahmoud Mahfouz, Danial Der- vovic, Manuela Veloso, and Tucker Balch. 2020. Get Real: Realism Metrics for Robust Limit Order Book Market Simulations. InProceedings of the 1st ACM International Conference on AI in Finance. arXiv:1912.04941

    2020 arXiv

  35. [43]

    Zhuohan Wang and Carmine Ventre. 2025. DiffVolume: Diffusion Models for Vol- ume Generation in Limit Order Books. InProceedings of the 6th ACM International Conference on AI in Finance. 587–595. arXiv:2508.08698

    2025 arXiv

  36. [44]

    Zhuohan Wang and Carmine Ventre. 2026. DiffLOB: Diffusion Models for Counterfactual Generation in Limit Order Books. InProceedings of the 35th International Joint Conference on Artificial Intelligence (IJCAI-ECAI 2026). arXiv:2602.03776

    2026

  37. [45]

    Magnus Wiese, Robert Knobloch, Ralf Korn, and Peter Kretschmer. 2020. Quant GANs: Deep Generation of Financial Time Series.Quantitative Finance20, 9 (2020). arXiv:1907.06673

    2020 arXiv

  38. [46]

    Ling Yang, Zhilong Zhang, Yang Song, Shenda Hong, Runsheng Xu, Yue Zhao, Wentao Zhang, Bin Cui, and Ming-Hsuan Yang. 2023. Diffusion models: A comprehensive survey of methods and applications.ACM computing surveys56, 4 (2023), 1–39

    2023

  39. [47]

    Wenliang Zhao, Lujia Bai, Yongming Rao, Jie Zhou, and Jiwen Lu. 2023. Unipc: A unified predictor-corrector framework for fast sampling of diffusion models. Advances in Neural Information Processing Systems36 (2023), 49842–49869

    2023

  40. [48]

    Zetao Zheng, Guoan Li, Deqiang Ouyang, Decui Liang, and Jie Shao. 2024. Limit Order Book Event Stream Prediction with Diffusion Model.Data Science and Engineering(2024). arXiv:2412.09631. 8

    2024 arXiv

  41. [2015]

    In Proceedings of the 32nd International Conference on Machine Learning

    Deep Unsupervised Learning using Nonequilibrium Thermodynamics. In Proceedings of the 32nd International Conference on Machine Learning. 2256–2265. arXiv:1503.03585

    arXiv

  42. [2020]

    InProceedings of the AAAI Conference on Artificial Intelligence, Vol

    Generating Realistic Stock Market Order Streams. InProceedings of the AAAI Conference on Artificial Intelligence, Vol. 34. 727–734

  43. [2022]

    Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps.Advances in neural information processing systems35 (2022), 5775–5787

    2022

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.