Triadic Dynamics Aware Diffusion Posterior Sampling for Inverse Problems:

Optimizing Guidance and Stochasticity Schedules

  ICML 2026
Junseo Bang1,*   Dong Ju Mun1,*   Hoigi Seo1   Seongmin Hong2   Se Young Chun1,2,3

1Dept. of Electrical & Computer Engineering  ·  2INMC  ·  3IPAI & AIIS, Seoul National University, Republic of Korea

*Equal contribution  ·  Correspondence: sychun@snu.ac.kr

arXiv Code BibTeX

Key Idea

Posterior sampling as an optimization problem of time-varying schedules

Generative posterior sampling for inverse problems usually consists of three main components: data consistency (DC) guidance, classifier-free guidance (CFG), and stochasticity. While prior arts have focused on how to develop each or all components, less attention has been given to how to schedule them, leading to heuristically fixed or partially adjusted suboptimal schedules. TriPS instead reformulates posterior sampling as an optimization problem of time-varying schedules and jointly optimizes the three schedules along a triadic trend.

TriPS key idea: the triadic coupling
The three components form a coupled triad: aggressive CFG early in sampling conflicts with DC guidance and slows the decay of the measurement residual, while calibrated stochasticity regularizes the off-manifold phenomenon, steering trajectories back toward higher-probability regions. These findings yield a single triadic scheduling trend, a monotonic decrease in β(t), increase in λ(t), and decrease in η(t).

DC guidance · β(t) ↓

High early to strongly enforce data consistency, then reduced to avoid over-enforcing it.

CFG · λ(t) ↑

Low early to suppress the guidance conflict, then increased to sharpen semantics.

Stochasticity · η(t) ↓

High early to regularize the off-manifold phenomenon, then annealed to reduce sampling error.

Qualitative Samples

Linear inverse problems (SD3.5-M)

For each sample, the top slider compares the measurement against our reconstruction, and the bottom slider compares FlowDPS against ours. Drag to compare, and browse with the arrows.

1–3 / 15

Drag the handle on any pair to reveal each side. Inpainting uses TriPS-T; the others use TriPS-G.

Analysis

Triadic Coupling Dynamics

We analyze the triadic coupling dynamics in posterior sampling, governed by DC guidance, CFG, and stochasticity. We formalize the early-stage conflict between DC guidance and CFG, and demonstrate how stochasticity regularizes sampling trajectories toward higher-probability regions.

Early stage guidance conflict
Early-stage guidance conflict. Since DC guidance and CFG originate from distinct objectives, their update directions are misaligned. As the CFG scale increases, this early-stage conflict intensifies, slowing the decay of the measurement residual and inducing semantic hallucinations that deviate from the measurement.
Stochasticity as a regularizer
Stochasticity as a regularizer. Stronger DC guidance or CFG drives sampling away from higher-probability trajectories, lowering its alignment with the score function, whereas appropriately scaled stochasticity consistently improves this alignment, suppressing artifacts and restoring perceptual fidelity.

Method

Triadic Schedule Optimization

To realize the triadic scheduling trend, TriPS comprises two complementary paradigms: a template-based schedule search that identifies robust schedule curves from a discrete family of functional forms, and a GRPO-based schedule optimization that captures complex temporal curves beyond the fixed functional templates.

TriPS method overview
(Left) TriPST explores a discrete search space defined by compact templates (Linear, Exp, Log) that satisfy the triadic scheduling trend (β(t)↓, λ(t)↑, η(t)↓), turning a high-dimensional schedule search into a low-dimensional selection. (Right) TriPSG enables continuous schedule discovery beyond fixed functional forms: a policy πθ samples coefficients from learnable Beta distributions to parameterize the schedules via Bernstein polynomials, strictly constraining each curve within a valid range, and is updated by rewards derived from the restored images.

TriPST · Template-based schedule search

A coarse grid search over a discrete template family {linear, exponential, logarithmic} that satisfies the triadic trend, maximizing a multi-objective utility of fidelity (PSNR) and perceptual quality (LPIPS). Provides a robust baseline and a warm start for GRPO.

TriPSG · GRPO-based schedule optimization

Each schedule is a Bernstein polynomial with coefficients sampled from Beta distributions, confining every curve to a physically valid range. The policy is optimized with a clipped GRPO objective and a hybrid IQA reward combining distortion and perceptual metrics.

Quantitative Comparison

Linear inverse problems (SD3.5-M)

Our experiments clearly demonstrate that TriPS-T consistently outperforms existing flow-based approaches across all evaluation metrics, and that TriPS-G further advances these results, significantly improving perceptual metrics while maintaining high measurement consistency.

Table 1: quantitative comparison
Quantitative comparison on linear inverse problems with the SD3.5-M flow matching prior (Table 1 of the paper).

Ablation

Reward-guided Perception–Distortion Control

Reward guided perception distortion control
By reweighting the distortion and perception terms of the hybrid reward, TriPSG navigates the perception-distortion trade-off. The optimized schedules align with the triadic scheduling trend while exhibiting fine-grained temporal variations, such as local non-monotonic fluctuations and magnitude shifts, that prove critical for pushing the perception-distortion Pareto frontier.

Cite

BibTeX

@misc{bang2026triadicdynamicsawarediffusion,
  title         = {Triadic Dynamics Aware Diffusion Posterior Sampling for Inverse
                   Problems: Optimizing Guidance and Stochasticity Schedules},
  author        = {Junseo Bang and Dong Ju Mun and Hoigi Seo and Seongmin Hong and Se Young Chun},
  year          = {2026},
  eprint        = {2605.26470},
  archivePrefix = {arXiv},
  primaryClass  = {cs.CV},
  url           = {https://arxiv.org/abs/2605.26470}
}