Talk:Diffusion model

Edit request: Addition of InDI (Inversion by Direct Iteration)

Latest comment: 7 days ago5 comments3 people in discussion

Hello, I would like to propose a small addition to this article to cover a recent approach to generative modeling and inverse problems called Inversion by Direct Iteration (InDI), published in Transactions on Machine Learning Research (2023) and recognized with an Outstanding Paper Award.

In accordance with Wikipedia's Conflict of Interest guidelines, I want to transparently disclose that I was involved in this research. I am requesting that an independent editor review the following suggestions and implement them if they find them to be a valuable and neutral addition to the page.

Scientifically, InDI is highly relevant to this article because it appeared concurrently with Flow Matching and Rectified Flow (late 2022/2023), but arrived at a virtually identical linear flow methodology from a completely different perspective. While Flow Matching originated from optimal transport and generative modeling, InDI approached it from the perspective of supervised image restoration—specifically, splitting an ill-posed inverse problem into smaller steps to avoid the "regression-to-the-mean" effect. The paper also showcases pure generation as a special case of this flow-based methodology.

I have provided two potential options for where this could fit naturally into the current text:

Option 1: In the "Flow-based diffusion model" section (under Rectified flow) Given the mathematical equivalence and concurrent timeline, a brief note could be added at the end of the "Rectified flow" subsection.

  • Proposed addition: "These linear flow formulations were concurrently discovered and adapted from a different perspective for supervised inverse problems. For example, Inversion by Direct Iteration (InDI) formulates image restoration by learning a residual flow ODE that iteratively reverses a linear interpolation between a degraded input and a high-quality target to avoid regression-to-the-mean. InDI also demonstrates pure generation as a special case of this deterministic flow-based methodology.[1]"

Option 2: In the "Other examples" subsection Alternatively, please consider adding InDI to the list of notable variants.

  • Current text: "Notable variants include Poisson flow generative model, consistency model, critically damped Langevin diffusion, GenPhys, cold diffusion, etc."
  • Proposed text: "Notable variants include Poisson flow generative model, consistency model, critically damped Langevin diffusion, GenPhys, cold diffusion, and Inversion by Direct Iteration (InDI), an approach developed concurrently to flow matching that learns an iterative restoration process from paired examples.[2]"

Thank you for your time and for reviewing this request. ~2026-18316-27 (talk) 14:57, 24 March 2026 (UTC) ~2026-18316-27 (talk) 14:57, 24 March 2026 (UTC)Reply

There seems to be a problem with the link you provided to this paper. Do you mean this one, instead: https://arxiv.org/abs/2303.11435 ? (That one's just a preprint, however.) Fiske (talk) 20:02, 24 March 2026 (UTC)Reply
Sorry! This is the right link to the TMLR published version:
https://openreview.net/forum?id=VmyFF5lL3F ~2026-18316-27 (talk) 03:43, 25 March 2026 (UTC)Reply
@~2026-18316-27: This paper has more than 200 citations in GoogleScholar today, so it's clearly getting attention. I've implemented Option 1, but I made two changes:
1. I replaced "concurrently" by "independently".
2. I replaced by "InDI also demonstrates pure generation as a special case of this deterministic flow-based methodology." by "InDI is effective for a variety of image restoration tasks." because I found no mention of pure generation in the cited source. If you have a source for that claim (or if I have misunderstood the paper), you can reopen this request to provide the information.
Longer term, it would be better to support this addition by adding a citation to a secondary source (e.g., review paper not by the authors) that discusses the importance of InDI.
I will close this request for now. Fiske (talk) 17:43, 29 May 2026 (UTC)Reply
Regarding pure generation: Section 6.1 ("A generative framework") explicitly details how the exact same formulation can be applied as a generative model by taking the low-quality input to the limit of pure Gaussian noise. Qualitative generation results and metrics (FID) on CelebA are presented in Figure 8 and discussed further in Section 6.2 / Figure 9(d). ~2026-43111-18 (talk) 05:20, 5 August 2026 (UTC)Reply

References

  1. ^ Delbracio, Mauricio; Milanfar, Peyman (2023). "Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration". Transactions on Machine Learning Research.
  2. ^ Delbracio, Mauricio; Milanfar, Peyman (2023). "Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration". Transactions on Machine Learning Research.

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