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arxiv: 2606.05649 · v1 · pith:3FG7DQ4Vnew · submitted 2026-06-04 · 📊 stat.CO · cs.LG

Diff2SP: Diffusion Models for Correlated Scenario Generation in Stochastic Programming

Haixiang Sun , Andrew Liu This is my paper

Pith reviewed 2026-06-27 23:03 UTC · model grok-4.3

classification 📊 stat.CO cs.LG
keywords diffusion modelsstochastic programmingscenario generationregret boundssample complexitydecision-aware generationpower systems
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The pith

Diff2SP trains diffusion models by embedding stochastic optimization objectives to produce decision-aware scenarios for stochastic programming.

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

The paper presents Diff2SP as a diffusion-based method that folds the downstream stochastic program directly into model training rather than treating scenario generation as a separate step. This design aims to produce scenarios that remain statistically realistic while also improving the quality of decisions made under uncertainty. A sympathetic reader would care because existing sampling methods often miss complex dependencies and supervised approaches restrict variety, whereas this framework claims to tie generation accuracy to optimization performance through explicit regret bounds and sample-complexity results that outperform GANs. The work validates these claims on both synthetic data and power-system instances.

Core claim

Diff2SP embeds stochastic optimization into the diffusion training process to generate scenarios that are statistically coherent and decision-aware. Regret bounds are established that link distributional accuracy to decision quality, along with sample complexity guarantees that demonstrate faster convergence compared to traditional generative models such as GANs. Validation on synthetic and power-system datasets confirms improvements in both statistical fidelity and optimization outcomes.

What carries the argument

Diff2SP, a diffusion-based generative framework whose training objective is augmented with the downstream stochastic program loss.

If this is right

  • Regret bounds connect the accuracy of the generated scenario distribution directly to the quality of decisions obtained from the stochastic program.
  • Sample complexity results indicate that Diff2SP requires fewer samples to achieve good performance than GAN-based alternatives.
  • Generated scenarios improve both statistical properties and downstream decision outcomes on power-system applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same embedding idea could be tested with other generative models whose training loops accept an auxiliary loss term.
  • In operational settings the approach might reduce the need for manual scenario filtering before feeding data into real-time optimizers.
  • Extensions could examine whether the regret guarantees remain stable when the stochastic program itself changes between training and deployment.

Load-bearing premise

The diffusion training objective can be augmented with the stochastic program loss in a differentiable way that permits derivation of the stated regret bounds and sample complexity results.

What would settle it

An experiment showing that decision quality or convergence speed on the power-system dataset does not exceed results from a standard GAN would falsify the central performance claims.

Figures

Figures reproduced from arXiv: 2606.05649 by Andrew Liu, Haixiang Sun.

Figure 1
Figure 1. Figure 1: Comparison between the ground-truth correlation matrix and the estimated cor [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Error rate vs Number of Scenarios [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of averaged generation between original data and generated data in [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance Comparison of Different Diffusion Model Variants Across Scenario [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
read the original abstract

Scenario generation is a critical component in stochastic programming (SP), as it directly influences the quality of decision-making under uncertainty. Existing approaches predominantly rely on either sampling-based techniques or supervised learning using neural networks. Sampling-based techniques often struggle to capture complex dependencies and rare but plausible events, while supervised learning requires fixed input-output pairs for training and is limited in its ability to generate a wide variety of realistic scenarios that are not restricted by predefined patterns or rules. To address these limitations, we introduce Diff2SP, a diffusion-based generative framework that incorporates downstream optimization objectives directly into scenario generation. Unlike conventional methods that treat scenario generation and decision-making as separate steps, Diff2SP embeds stochastic optimization into the training process, enabling the generation of scenarios that are both statistically coherent and decision-aware. To formally justify this optimization-aware design, we establish a regret bounds that link distributional accuracy to decision quality, and establish sample complexity guarantees showing faster convergence than traditional generative models such as GANs. Empirical results on both synthetic and power-system datasets validate these theoretical insights, demonstrating that Diff2SP consistently improves both statistical fidelity and downstream optimization outcomes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces Diff2SP, a diffusion-based generative framework for scenario generation in stochastic programming that embeds the downstream stochastic optimization objective directly into the diffusion training process. It claims to derive regret bounds linking distributional accuracy to decision quality and sample-complexity guarantees showing faster convergence than GANs, with empirical validation on synthetic and power-system datasets.

Significance. If the regret bounds and sample-complexity results can be rigorously established, the work would offer a principled integration of optimization awareness into generative modeling for SP, with potential impact on applications requiring decision-aware scenarios such as power systems. The explicit comparison to GANs and the focus on correlated scenario generation are strengths if the theoretical claims hold.

major comments (2)
  1. [Abstract] Abstract: the claimed regret bounds are presented as justification for the optimization-aware design, yet no derivation, reparameterization mechanism, or straight-through estimator is supplied for differentiating the stochastic program loss through the iterative diffusion sampler; without this construction the bounds cannot be verified to hold.
  2. [Abstract] Abstract: the sample-complexity guarantees versus GANs are asserted without listing the required regularity conditions (Lipschitz constants of the SP loss, bounded variance of the reverse process, etc.); the abstract supplies no information on these hypotheses, making it impossible to confirm that the claimed improvement is not circular with quantities already fitted in the training loss.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'establish a regret bounds' is grammatically incorrect and should be revised to 'establish regret bounds'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment point by point below and indicate the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claimed regret bounds are presented as justification for the optimization-aware design, yet no derivation, reparameterization mechanism, or straight-through estimator is supplied for differentiating the stochastic program loss through the iterative diffusion sampler; without this construction the bounds cannot be verified to hold.

    Authors: The regret bounds are formally derived in Section 4 by relating the distributional discrepancy (in Wasserstein distance) to the decision regret of the downstream stochastic program. However, the referee correctly notes that the abstract and surrounding text do not explicitly detail the reparameterization of the iterative diffusion sampler or the straight-through estimator required to differentiate the SP loss. We will revise the manuscript to add this construction in Section 3 (model description) and an expanded appendix, thereby making the link between the bounds and the training procedure verifiable. revision: yes

  2. Referee: [Abstract] Abstract: the sample-complexity guarantees versus GANs are asserted without listing the required regularity conditions (Lipschitz constants of the SP loss, bounded variance of the reverse process, etc.); the abstract supplies no information on these hypotheses, making it impossible to confirm that the claimed improvement is not circular with quantities already fitted in the training loss.

    Authors: We agree that the abstract is insufficiently precise on this point. Section 5 derives the sample-complexity results under the standard assumptions of Lipschitz continuity of the SP loss (constant L) and bounded second moments of the reverse diffusion process; these conditions are independent of the parameters fitted during training. We will revise the abstract to reference these hypotheses and add an explicit statement in Section 5 clarifying that the faster rates relative to GANs follow from the optimization-aware objective rather than from any circular dependence on fitted quantities. revision: yes

Circularity Check

0 steps flagged

No circularity; claimed bounds presented as independent formal justification

full rationale

The abstract asserts that regret bounds and sample-complexity results are established to justify embedding the stochastic program into diffusion training, but supplies no equations, no self-citations, and no derivation steps that reduce the bounds to quantities already present in the training loss by construction. No fitted-input-called-prediction, self-definitional, or ansatz-smuggling patterns are visible. The derivation is therefore treated as self-contained pending the full manuscript.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central claim rests on the unshown derivation of regret bounds and on the assumption that the diffusion sampler can be trained end-to-end with a non-differentiable or black-box stochastic program.

pith-pipeline@v0.9.1-grok · 5721 in / 1143 out tokens · 15636 ms · 2026-06-27T23:03:34.731439+00:00 · methodology

discussion (0)

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Reference graph

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