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arxiv: 2211.01095 · v3 · submitted 2022-11-02 · 💻 cs.LG · cs.CV

Recognition: 2 theorem links

· Lean Theorem

DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models

Cheng Lu , Yuhao Zhou , Fan Bao , Jianfei Chen , Chongxuan Li , Jun Zhu
Authors on Pith no claims yet

Pith reviewed 2026-05-16 07:50 UTC · model grok-4.3

classification 💻 cs.LG cs.CV
keywords diffusion probabilistic modelsguided samplingfast samplingDPM-Solver++high-order ODE solverDDIMtext-to-image generationlatent diffusion
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The pith

DPM-Solver++ generates high-quality guided samples from diffusion models in 15 to 20 steps

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

Diffusion models for high-resolution image synthesis need guided sampling with large guidance scales to reach best quality, yet the standard fast sampler DDIM still requires 100 to 250 steps. Earlier high-order ODE solvers that speed up unguided sampling become unstable or slower than DDIM once guidance grows large. The paper introduces DPM-Solver++ that solves the diffusion ODE from the data-prediction model, applies thresholding to keep solutions inside the training distribution, and adds a multistep variant that shrinks the effective step size. Experiments confirm that this combination produces high-quality samples for both pixel-space and latent-space models in only 15 to 20 steps.

Core claim

Previous high-order fast samplers for diffusion ODEs suffer from instability issues and become slower than DDIM when the guidance scale grows large. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matching the training data distribution. Its multistep variant addresses the instability by reducing the effective step size, enabling high-quality guided sampling in 15 to 20 steps.

What carries the argument

DPM-Solver++, a high-order diffusion ODE solver that uses the data-prediction formulation together with thresholding and a multistep variant to restore stability under large guidance scales

If this is right

  • Guided sampling reaches high quality with far fewer steps than DDIM for both pixel and latent DPMs.
  • High-order solvers become usable for conditional generation once formulated around data prediction and thresholding.
  • Multistep correction stabilizes the solver without increasing the total number of function evaluations.
  • Computational cost of text-to-image generation drops sharply while preserving sample quality.

Where Pith is reading between the lines

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

  • The same data-prediction and thresholding choices may stabilize solvers in other conditional generation settings beyond classifier-free guidance.
  • Fifteen-step sampling could open real-time or interactive uses for large diffusion models.
  • Adaptive selection between single-step and multistep modes might further reduce average compute across varying guidance scales.

Load-bearing premise

The data-prediction formulation combined with thresholding and the multistep variant reliably removes instability at large guidance scales.

What would settle it

Running DPM-Solver++ for 15 steps at high guidance scale on a standard text-to-image benchmark and observing that sample quality falls below DDIM or exhibits visible artifacts or divergence.

read the original abstract

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of DPMs is guided sampling, which usually needs a large guidance scale to obtain the best sample quality. The commonly-used fast sampler for guided sampling is DDIM, a first-order diffusion ODE solver that generally needs 100 to 250 steps for high-quality samples. Although recent works propose dedicated high-order solvers and achieve a further speedup for sampling without guidance, their effectiveness for guided sampling has not been well-tested before. In this work, we demonstrate that previous high-order fast samplers suffer from instability issues, and they even become slower than DDIM when the guidance scale grows large. To further speed up guided sampling, we propose DPM-Solver++, a high-order solver for the guided sampling of DPMs. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matches training data distribution. We further propose a multistep variant of DPM-Solver++ to address the instability issue by reducing the effective step size. Experiments show that DPM-Solver++ can generate high-quality samples within only 15 to 20 steps for guided sampling by pixel-space and latent-space DPMs.

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 / 2 minor

Summary. The paper proposes DPM-Solver++, a high-order solver for the guided sampling of diffusion probabilistic models (DPMs). It solves the diffusion ODE using a data-prediction formulation with thresholding and introduces a multistep variant to mitigate instability observed in prior high-order solvers at large guidance scales. Experiments are presented claiming that DPM-Solver++ generates high-quality samples in only 15-20 steps for both pixel-space and latent-space DPMs, outperforming DDIM and earlier high-order methods.

Significance. If the stability and speedup claims hold, the work would provide a practical acceleration for guided sampling in large-scale DPMs, which is central to text-to-image applications. The derivation is parameter-free and builds directly on the standard diffusion ODE without fitting additional parameters; the explicit algorithmic choices (data prediction, thresholding, multistep schedule) are a strength that could be reproducible if code and exact schedules are released.

major comments (2)
  1. [Abstract] Abstract: the claim that prior high-order solvers become unstable and slower than DDIM at large guidance scales is presented without quantitative metrics, error bars, or ablation details on how instability was measured or controlled; this weakens the motivation for the multistep fix.
  2. [Section 3 (Multistep DPM-Solver++)] The multistep variant is asserted to address instability by reducing effective step size, yet no derivation is given showing how the predictor-corrector or extrapolation coefficients achieve this reduction while preserving high-order accuracy; the central stability claim therefore rests on an unverified assumption about the specific multistep schedule.
minor comments (2)
  1. Add error bars or statistics over multiple random seeds to all sampling-quality plots and tables to support the 15-20 step claims.
  2. Clarify the exact thresholding implementation and its interaction with the data-prediction model in the main text rather than deferring all details to the appendix.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below with clarifications and indicate the revisions planned for the next version of the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that prior high-order solvers become unstable and slower than DDIM at large guidance scales is presented without quantitative metrics, error bars, or ablation details on how instability was measured or controlled; this weakens the motivation for the multistep fix.

    Authors: We agree that the abstract would be strengthened by explicit quantitative support. In the revised manuscript we will expand the abstract to include concrete metrics: FID scores and sampling wall-clock times comparing a prior high-order solver (DPM-Solver) against DDIM at guidance scale 7.5, together with standard deviations computed over three independent runs. We will also add a short description in Section 4 of how instability was quantified (sample divergence measured by FID increase beyond a threshold and per-step norm of the update exceeding a stability bound). revision: yes

  2. Referee: [Section 3 (Multistep DPM-Solver++)] The multistep variant is asserted to address instability by reducing effective step size, yet no derivation is given showing how the predictor-corrector or extrapolation coefficients achieve this reduction while preserving high-order accuracy; the central stability claim therefore rests on an unverified assumption about the specific multistep schedule.

    Authors: We appreciate the request for a rigorous derivation. In the revised Section 3 we will insert a new subsection that derives the effective step-size reduction from the predictor-corrector coefficients and the linear extrapolation formula. Using Taylor expansion of the data-prediction ODE solution, we will show that the local truncation error order is retained while the leading error term is scaled by a factor proportional to the reduced effective step size. The derivation will be parameter-free and will directly reference the multistep schedule already given in Algorithm 2. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation starts from standard diffusion ODE with explicit algorithmic choices

full rationale

The paper starts from the standard diffusion ODE and introduces explicit algorithmic components (data-prediction formulation, thresholding, and a multistep variant) to improve guided sampling. These choices are presented as design decisions rather than parameters fitted to the target result or definitions that presuppose the claimed performance. No load-bearing equation or step reduces by construction to its own inputs, and any self-citations to prior DPM-Solver work are not used to justify the new stabilization claims for large guidance scales. The central claims rest on empirical validation rather than self-referential reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the standard reformulation of diffusion sampling as an ODE and the assumption that thresholding can enforce consistency with the training distribution; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Diffusion probabilistic models admit an ODE formulation whose solution yields the generative process.
    This is the standard continuous-time view of DPMs used throughout the literature.

pith-pipeline@v0.9.0 · 5553 in / 1136 out tokens · 31784 ms · 2026-05-16T07:50:42.794854+00:00 · methodology

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    A A DDITIONAL PROOFS A.1 P ROOF OF PROPOSITION 4.1 Taking derivative w.r.t.t in Eq. (8) yields dxt dt = dσt dt xs σs + dσt dt Z λt λs eλ ˆxθ(ˆxλ, λ)dλ + dλt dt σteλt ˆxθ(ˆxλt , λt) = dσt dt xt σt + dλt dt σteλt ˆxθ(ˆxλt , λt) = f(t) + g2(t) 2σ2 t xt σt − αtg2(t) 2σ2 t xθ(xt, t), where the last inequality follows from the definitions f(t) = d log αt dt , g...

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    r1 (ϵθ(xr, r) − ϵθ(xs, s)). (37) SDE-DPM-Solver++2M We have 2αt Z λt λs e−2(λt−λ)xθ(xλ, λ)dλ (38) ≈ 2αte−2λt Z λt λs e2λdλ ! xθ(xs, s) + 2αte−2λt Z λt λs e2λ(λ − λs)dλ ! xθ(xr, r) − xθ(xs, s) r1h (39) = αt(1 − e−2h)xθ(xs, s) + αt e−2h − 1 + 2h 2h xθ(xr, r) − xθ(xs, s) r1 (40) We can also applying the same approximation as in Lu et al. (2022) by e−2h − 1 +...

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    Let ∆i := ∥˜xti − xti ∥. Taylor’s expansion yields xti − αti αti−1 xti−1 − αti(e−hi − 1)xθ(xti−1 , ti−1) − αti −e−hi − hi + 1 x(1) θ (xti−1 , ti−1) ≤ Ch 3 i , where C is a constant depends on x(2) θ . Also note that x(1) θ (xti−1 , ti−1) − 1 hi−1 xθ(xti−1 , ti−1) − xθ(xti−2 , ti−2) ≤ Ch i, Since ri is bounded away from zero, and e−hi = 1 − hi + h2 i /2 + ...

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    A beautiful castle beside a waterfall in the woods, by Josef Thoma, matte painting, trending on artstation HQ

    is designed for uniform λ (the intermediate time steps are a half of the step size w.r.t. λ), we also convert the intermediate time steps to ensure all the time steps are uniform t. We find that such conversion can improve the sample quality of both the singlestep DPM-Solver the singlestep DPM-Solver++. We run NFE in 10, 15, 20, 25 for the high-order solv...

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    Guidance scale is 7.5, which is the recommended setting for stable-diffusion (Rombach et al., 2022)

    10.18 8.63 8.20 7.98 \ \ \ DPM-Solver++(S) (ours) 9.18 8.17 7.77 7.56 \ \ \ DPM-Solver++(M) (ours) 9.19 8.47 8.17 8.07 \ \ \ Yes DDIM (Song et al., 2021a) 11.19 9.20 8.42 8.05 7.65 7.59 7.63 DPM-Solver++(S) (ours) 9.23 8.18 7.81 7.60 \ \ \ DPM-Solver++(M) (ours) 9.28 8.56 8.28 8.18 \ \ \ Table 4: Sample quality measured by MSE↓ on COCO2014 validation set ...

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    23 Preprint NFE = 10 DPM-Solver++(2M) (ours) DDPM (Ho et al.,

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