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arxiv: 2010.02502 · v4 · submitted 2020-10-06 · 💻 cs.LG · cs.CV

Denoising Diffusion Implicit Models

Jiaming Song , Chenlin Meng , Stefano Ermon This is my paper

Pith reviewed 2026-05-24 14:39 UTC · model grok-4.3

classification 💻 cs.LG cs.CV
keywords denoising diffusionimplicit modelssampling accelerationnon-Markovian processesimage generationlatent space interpolationgenerative models
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The pith

Denoising diffusion implicit models produce high-quality samples using the same training as DDPMs but with far fewer sampling steps via non-Markovian processes.

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

The paper shows that non-Markovian diffusion processes can be defined to match the training objective of standard DDPMs while making the reverse generative process much quicker to run. This addresses the slow sampling that has limited diffusion models in practice, since each sample normally requires simulating many steps of a Markov chain. A sympathetic reader would care because the change keeps training unchanged yet cuts the number of steps needed at generation time by a large factor. If the construction holds, it opens a direct way to balance speed against quality without retraining and supports operations like interpolation inside the model's latent space.

Core claim

We construct a class of non-Markovian diffusion processes that lead to the same training objective as DDPMs, but whose reverse process can be much faster to sample from. DDIMs therefore allow high-quality samples to be produced 10 times to 50 times faster in wall-clock time, let users trade computation for sample quality, and support semantically meaningful image interpolation directly in the latent space.

What carries the argument

The non-Markovian diffusion process, which is constructed to share the identical training objective with the Markovian DDPM forward process while permitting accelerated reverse sampling.

If this is right

  • Samples of comparable quality can be generated in 10x to 50x less wall-clock time than with DDPMs.
  • Users can choose fewer or more sampling steps to trade computation directly against sample quality.
  • Image interpolation performed in the latent space produces semantically meaningful results.
  • The generative process remains iterative and implicit but no longer requires the full Markov chain simulation.

Where Pith is reading between the lines

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

  • The same non-Markovian construction might be applied to other iterative generative models that currently rely on Markovian forward processes.
  • Fewer sampling steps could make diffusion-based generation feasible inside interactive or real-time applications.
  • Latent-space interpolation raises the possibility of controlled editing or morphing tasks without additional supervision.

Load-bearing premise

Non-Markovian diffusion processes can be built that keep exactly the same training objective as the Markovian DDPM forward process yet allow a faster reverse sampling procedure.

What would settle it

Training a model on the DDIM objective and then measuring whether its few-step samples match the quality of a standard DDPM run with hundreds of steps on the same data.

Figures

Figures reproduced from arXiv: 2010.02502 by Chenlin Meng, Jiaming Song, Stefano Ermon.

Figure 1
Figure 1. Figure 1: Graphical models for diffusion (left) and non-Markovian (right) inference models. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Graphical model for accelerated generation, where [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: CIFAR10 and CelebA samples with dim(τ ) = 10 and dim(τ ) = 100. 5.1 SAMPLE QUALITY AND EFFICIENCY In [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Hours to sample 50k images with one Nvidia 2080 Ti GPU and samples at different steps. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Samples from DDIM with the same random xT and different number of steps. quality are encoded in the parameters, as longer sample trajectories gives better quality samples but do not significantly affect the high-level features. We show more samples in Appendix D.4. 5.3 INTERPOLATION IN DETERMINISTIC GENERATIVE PROCESSES [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Interpolation of samples from DDIM with dim(τ ) = 50. Since the high level features of the DDIM sample is encoded by xT , we are interested to see whether it would exhibit the semantic interpolation effect similar to that observed in other implicit proba￾8 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: CIFAR10 samples from 1000 step DDPM, 1000 step DDIM and 100 step DDIM. [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: CelebA samples from 1000 step DDPM, 1000 step DDIM and 100 step DDIM. [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: CelebA samples from DDIM with the same random [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Church samples from 100 step DDPM and 100 step DDIM. [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: More interpolations from the CelebA DDIM with [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: More interpolations from the Bedroom DDIM with [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: More interpolations from the Church DDIM with [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
read the original abstract

Denoising diffusion probabilistic models (DDPMs) have achieved high quality image generation without adversarial training, yet they require simulating a Markov chain for many steps to produce a sample. To accelerate sampling, we present denoising diffusion implicit models (DDIMs), a more efficient class of iterative implicit probabilistic models with the same training procedure as DDPMs. In DDPMs, the generative process is defined as the reverse of a Markovian diffusion process. We construct a class of non-Markovian diffusion processes that lead to the same training objective, but whose reverse process can be much faster to sample from. We empirically demonstrate that DDIMs can produce high quality samples $10 \times$ to $50 \times$ faster in terms of wall-clock time compared to DDPMs, allow us to trade off computation for sample quality, and can perform semantically meaningful image interpolation directly in the latent space.

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 manuscript introduces denoising diffusion implicit models (DDIMs), a generalization of DDPMs that replaces the Markovian forward diffusion with a family of non-Markovian processes whose marginals q(x_t | x_0) remain identical. This permits reuse of the identical trained denoising network while allowing a non-Markovian reverse process that supports substantially larger steps, yielding 10–50× wall-clock speedups, a compute–quality tradeoff, and direct latent-space interpolation.

Significance. If the marginal-equivalence construction is exact, the result is significant: it removes the need to retrain when accelerating sampling and directly addresses the primary practical bottleneck of DDPMs. The additional capabilities (trade-off control and interpolation) further increase the method’s utility for downstream generative tasks.

major comments (2)
  1. [§3.2] §3.2 (construction of the non-Markovian process): the claim that any variance schedule β_t yields identical marginals q(x_t | x_0) to the DDPM forward process must be shown to hold without additional restrictions on the schedule; otherwise the same trained weights cannot be reused for accelerated sampling without distribution shift.
  2. [§4] §4 (experiments): the reported 10–50× wall-clock speedups and quality claims lack any description of the exact sampling schedules, hardware, batch sizes, number of runs, or variance across seeds; without these the empirical support for the central speedup claim cannot be assessed.
minor comments (2)
  1. [§3] Notation for the implicit reverse process (Eq. (7) or equivalent) should explicitly distinguish the deterministic limit (η=0) from the stochastic case to avoid reader confusion about when the process remains probabilistic.
  2. [§4] Figure 3 (interpolation examples) would benefit from a quantitative metric (e.g., LPIPS or FID between interpolated and endpoint images) rather than relying solely on visual inspection.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. Below we respond point-by-point to the two major comments. We will revise the manuscript to address both concerns.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (construction of the non-Markovian process): the claim that any variance schedule β_t yields identical marginals q(x_t | x_0) to the DDPM forward process must be shown to hold without additional restrictions on the schedule; otherwise the same trained weights cannot be reused for accelerated sampling without distribution shift.

    Authors: Section 3.2 constructs the non-Markovian forward process by defining q(x_{t-1}|x_t,x_0) so that the marginal q(x_t|x_0) is identical to the DDPM marginal for any schedule {β_t} that satisfies the standard DDPM conditions (0<β_t<1 and the usual cumulative product definitions). The derivation uses only the law of total probability and the Gaussian parameterization already present in DDPMs; no further restrictions on the schedule are imposed. Consequently the training objective remains unchanged and the same network weights can be reused. We will add an explicit sentence in §3.2 stating that the marginal equivalence holds for arbitrary valid β schedules. revision: partial

  2. Referee: [§4] §4 (experiments): the reported 10–50× wall-clock speedups and quality claims lack any description of the exact sampling schedules, hardware, batch sizes, number of runs, or variance across seeds; without these the empirical support for the central speedup claim cannot be assessed.

    Authors: We agree that the experimental section is missing these reproducibility details. In the revised manuscript we will report: (i) the exact DDIM sampling schedules (number of steps and η values) used for each speedup factor, (ii) the hardware (GPU model and count), (iii) batch sizes, and (iv) mean and standard deviation of FID/IS over at least three independent runs with different random seeds. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation of non-Markovian equivalence is self-contained

full rationale

The paper derives a family of non-Markovian forward processes whose marginal distributions at each timestep match those of the DDPM Markov chain, thereby preserving the identical variational lower bound training objective for the shared denoising network. This equivalence follows directly from the closed-form expressions for the forward process means and variances (standard Gaussian conditioning) without reference to the reverse sampling speed or empirical outcomes. The accelerated reverse sampling is then obtained by choosing larger implicit steps in the non-Markovian chain, a consequence rather than an input. No equations reduce a prediction to a fitted parameter, no self-citation supplies the uniqueness of the construction, and the central claim remains independently verifiable from the stated assumptions on the diffusion schedule.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields minimal ledger entries; the method inherits standard diffusion assumptions without introducing new fitted parameters or entities in the provided text.

axioms (1)
  • domain assumption The forward process gradually adds noise to data in a manner compatible with a learned reverse process.
    Implicit in the statement that DDIMs share the same training objective as DDPMs.

pith-pipeline@v0.9.0 · 5678 in / 1136 out tokens · 21977 ms · 2026-05-24T14:39:11.967551+00:00 · methodology

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