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Dual-Solver: A Generalized ODE Solver for Diffusion Models with Dual Prediction

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.5Download Report PDF
Generative ModelsDiffusion ModelsFast SamplingODE Solver
Abstract:

Diffusion models deliver state-of-the-art image quality. However, sampling is costly at inference time because it requires many model evaluations (number of function evaluations, NFEs). To reduce NFEs, classical ODE multistep methods have been adopted. Yet differences in the choice of prediction type (noise/data/velocity) and integration domain (half log-SNR/noise-to-signal ratio) lead to different outcomes. We introduce Dual-Solver, which generalizes multistep samplers by introducing learnable parameters that continuously (i) interpolate among prediction types, (ii) select the integration domain, and (iii) adjust the residual terms. It maintains the traditional predictor-corrector structure and guarantees second-order local accuracy. These parameters are learned with a classification-based objective using a frozen pretrained classifier (e.g., ViT or CLIP). On ImageNet class-conditional generation (DiT, GM-DiT) and text-to-image (SANA, PixArt-α\alpha), Dual-Solver improves FID and CLIP scores in the low-NFE regime (3≤3\le NFE ≤9\le 9) across backbones.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces Dual-Solver, a generalized ODE solver framework with learnable parameters that interpolate among prediction types, select integration domains, and adjust residual terms. It resides in the 'Learned and Adaptive ODE Solvers' leaf, which contains seven papers total (including this one). This leaf sits within the broader 'ODE Solver Design and Optimization' branch, indicating a moderately populated research direction focused on data-driven solver design rather than purely analytical methods. The taxonomy shows this is an active but not overcrowded subfield, with sibling papers exploring differentiable solver search, bespoke non-stationary solvers, and adaptive solver selection strategies.

The taxonomy reveals neighboring leaves include 'High-Order and Exponential Integrators' (seven papers using fixed analytical methods like DPM-Solver) and 'Optimized Time Discretization and Scheduling' (three papers focusing on step schedules). The 'Learned and Adaptive ODE Solvers' leaf explicitly excludes fixed analytical solvers, positioning Dual-Solver among methods that optimize solver parameters or structures via training. Nearby branches like 'Trajectory and Flow Modeling' (seven papers on consistency models and rectified flows) and 'Distillation and Model Compression' (one paper) represent alternative acceleration paradigms that modify the generative process itself rather than the numerical solver, highlighting Dual-Solver's focus on solver-level innovation.

Among three analyzed contributions, the core 'Dual-Solver framework' examined ten candidates and found one potentially refutable prior work, suggesting some overlap in the limited search scope of twenty-two papers. The 'classification-based parameter learning strategy' examined ten candidates with zero refutations, indicating relative novelty within the sampled literature. The 'log-linear domain transformation' examined only two candidates with no refutations, though the small sample limits confidence. These statistics reflect a targeted semantic search, not an exhaustive review, so the presence of one refutable candidate for the main contribution signals that similar learnable solver ideas exist in the immediate neighborhood.

Based on the limited search scope of twenty-two semantically related papers, Dual-Solver appears to occupy a recognizable niche within learned ODE solvers, with at least one closely related prior work among the candidates examined. The taxonomy context shows this is a moderately active research direction with established sibling methods, suggesting incremental refinement rather than a completely unexplored area. The analysis does not cover the full breadth of diffusion acceleration literature, so additional overlapping work may exist beyond the top-K semantic matches examined here.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
22
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: Accelerating diffusion model sampling with learned ODE solvers. The field has evolved into a rich landscape of complementary approaches, each targeting different aspects of the sampling bottleneck. At the highest level, the taxonomy reveals several major directions: ODE Solver Design and Optimization focuses on crafting better numerical integrators, often drawing on classical methods like exponential integrators (Exponential Integrator[1]) or higher-order schemes (DPM-Solver[5], DPM-Solver++[2]); Trajectory and Flow Modeling reshapes the underlying generative paths to be more amenable to fast sampling; Hybrid and Stochastic Sampling Methods blend deterministic ODE trajectories with carefully tuned noise; Distillation and Model Compression transfer multi-step sampling into fewer steps or even single-step generators (Consistency Trajectory Models[11]); and Specialized Acceleration Techniques exploit domain structure, such as reusing intermediate computations (Reuse Attention Maps[24]) or optimizing time-step schedules (Optimized Time Steps[10]). Additional branches cover Theoretical Foundations, which provide convergence guarantees and error bounds, and Domain-Specific Applications that tailor solvers to audio, video, or other modalities (AudioTurbo[30], AudioLCM[39]). Within ODE Solver Design and Optimization, a particularly active subarea is Learned and Adaptive ODE Solvers, where methods move beyond fixed numerical schemes to data-driven or search-based designs. For instance, Differentiable Solver Search[16] and Bespoke Non-Stationary Solvers[38] learn solver parameters or structures directly from training data, while S4S[6] and GAS[47] adapt solver behavior on-the-fly. Dual-Solver[0] sits naturally in this cluster, proposing a dual-solver framework that combines learned components with classical ODE integration principles. Compared to nearby works like Improved Integration Approximation[31] or Averaging Derivatives[14], which refine approximation quality through analytical insights, Dual-Solver[0] emphasizes the synergy between two complementary solvers to balance speed and accuracy. This positions it alongside other adaptive strategies (ODE-DPS[3], Fast ODE 5 Steps[4]) that dynamically adjust solver choices, yet it distinguishes itself by explicitly orchestrating multiple solvers rather than selecting a single adaptive path.

Claimed Contributions

Dual-Solver: A generalized ODE solver with learnable parameters

The authors propose Dual-Solver, a generalized ODE solver for diffusion models that introduces three types of learnable parameters: γ for interpolating among noise, data, and velocity predictions; τ for selecting between log and linear integration domains; and κ for adjusting residual terms while maintaining second-order accuracy.

10 retrieved papers
Can Refute
Classification-based parameter learning strategy

The authors introduce a classification-based learning approach that optimizes solver parameters using pretrained classifiers (e.g., ViT or CLIP) without requiring target samples from a teacher solver, unlike regression-based methods that typically need many high-NFE target samples.

10 retrieved papers
Log-linear domain transformation with parameter τ

The authors develop a log-linear transformation parameterized by τ that interpolates between linear (τ→0) and logarithmic (τ=1) integration domains, allowing flexible weighting of the integrand in the ODE solver formulation.

2 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Dual-Solver: A generalized ODE solver with learnable parameters

The authors propose Dual-Solver, a generalized ODE solver for diffusion models that introduces three types of learnable parameters: γ for interpolating among noise, data, and velocity predictions; τ for selecting between log and linear integration domains; and κ for adjusting residual terms while maintaining second-order accuracy.

Contribution

Classification-based parameter learning strategy

The authors introduce a classification-based learning approach that optimizes solver parameters using pretrained classifiers (e.g., ViT or CLIP) without requiring target samples from a teacher solver, unlike regression-based methods that typically need many high-NFE target samples.

Contribution

Log-linear domain transformation with parameter τ

The authors develop a log-linear transformation parameterized by τ that interpolates between linear (τ→0) and logarithmic (τ=1) integration domains, allowing flexible weighting of the integrand in the ODE solver formulation.

Table of Contents