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arxiv: 2605.18204 · v1 · pith:LZKXYAL5new · submitted 2026-05-18 · 📊 stat.ML · cs.LG

Forward-Learned Discrete Diffusion: Learning how to noise to denoise faster

Grigory Bartosh , Teodora Pandeva , Sushrut Karmalkar , Javier Zazo This is my paper

Pith reviewed 2026-05-20 00:21 UTC · model grok-4.3

classification 📊 stat.ML cs.LG
keywords discrete diffusionlearnable forward processnon-Markovian diffusionfew-step generationfactorized reverse processvariational traininggenerative modeling
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The pith

By learning the forward noising process as non-Markovian, discrete diffusion keeps its reverse process factorized yet matches the target in fewer steps.

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

Standard discrete diffusion fixes a Markovian forward chain, which forces the factorized reverse process to need many steps to approximate the data distribution well. This paper instead makes the forward process itself learnable in a non-Markovian formulation, with trainable marginal and posterior distributions. The reverse process can therefore stay factorized while still matching the target that the learned noising defines. End-to-end training under the usual variational objective then produces higher-quality samples for any fixed number of sampling steps. A sympathetic reader would care because the change promises to cut the expensive long sampling runs that currently limit discrete diffusion on text, images, and other discrete data.

Core claim

Forward-Learned Discrete Diffusion replaces the fixed Markovian forward chain with a learnable non-Markovian noising process whose marginal and posterior distributions are also optimized. This construction keeps the generative reverse process factorized while allowing it to match the target distribution induced by the learned forward process. All parameters are trained jointly under the standard variational bound, and experiments across benchmarks show that the resulting model yields higher-quality samples than conventional discrete diffusion when both use the same reverse parameterization and the same small number of sampling steps.

What carries the argument

A learnable non-Markovian forward process whose marginal and posterior distributions are optimized so the factorized reverse process matches the induced target.

If this is right

  • For any fixed number of sampling steps the model produces higher-quality samples than conventional discrete diffusion using the same reverse parameterization.
  • The generative process remains factorized while matching the target distribution induced by the learned noising.
  • All forward and reverse parameters are trained end-to-end under the standard variational objective.
  • The gap between the model distribution and the target is reduced, enabling few-step generation without altering the reverse form.
  • The improvement holds across multiple benchmarks when the reverse parameterization is held constant.

Where Pith is reading between the lines

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

  • The same learnable-forward idea could be tested in continuous diffusion to see whether it likewise shortens the required number of denoising steps.
  • Because the forward schedule is now data-driven, the method might automatically adapt diffusion length to dataset complexity without manual tuning.
  • Combining the approach with existing acceleration tricks such as step distillation could compound the reduction in sampling cost.
  • If the learned non-Markovian structure proves stable, it may extend naturally to other discrete generative settings such as molecular graphs or symbolic sequences.

Load-bearing premise

A non-Markovian formulation with learnable marginal and posterior distributions lets the factorized generative process match the target defined by the learned noising process.

What would settle it

On a standard benchmark, measure sample quality at a fixed small number of reverse steps; if the learned-forward model does not outperform the fixed-forward baseline under identical reverse parameterization, the central claim fails.

Figures

Figures reproduced from arXiv: 2605.18204 by Grigory Bartosh, Javier Zazo, Sushrut Karmalkar, Teodora Pandeva.

Figure 1
Figure 1. Figure 1: Training data distribution and learned dynamics for a mixture of two Gaussians. [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Learned dynamics for Binarized MNIST dataset. Generative process starts from prior [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
read the original abstract

Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized distributions, which makes it difficult for the model to learn the target process in a small number of steps and necessitates a long, computationally expensive sampling procedure. To reduce the gap between the target and model distributions and enable few-step generation, we propose Forward-Learned Discrete Diffusion (FLDD), which introduces discrete diffusion with a learnable forward (noising) process. Rather than fixing a Markovian forward chain, we adopt a non-Markovian formulation with learnable marginal and posterior distributions. This allows the generative process to remain factorized while matching the target defined by the noising process. We train all parameters end-to-end under the standard variational objective. Experiments on various benchmarks show that, for a given number of sampling steps, our approach produces a higher quality samples than conventional discrete diffusion models using the same reverse parameterization.

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

1 major / 1 minor

Summary. The paper proposes Forward-Learned Discrete Diffusion (FLDD), which replaces the fixed Markovian forward process in discrete diffusion models with a non-Markovian formulation whose marginal q(x_t | x_0) and posterior q(x_{t-1} | x_t, x_0) are learned jointly with the reverse process. The claim is that this allows the unchanged factorized reverse parameterization to match a better-defined target distribution under the standard variational objective, yielding higher-quality samples for any fixed number of sampling steps. Experiments on various benchmarks are reported to support the improvement over conventional discrete diffusion.

Significance. If the learned forward distributions remain internally consistent and the reported gains prove robust across datasets and metrics, the method could improve the practical efficiency of discrete diffusion by reducing the number of reverse steps required without altering the reverse network architecture. The end-to-end training under a standard variational bound and the direct comparison to fixed-forward baselines constitute concrete, falsifiable contributions.

major comments (1)
  1. [Method (non-Markovian forward process and training objective)] The non-Markovian formulation defines learnable marginal and posterior distributions whose consistency is required for the target distribution to be well-defined. The manuscript does not describe an explicit consistency constraint, reparameterization, or regularization term that enforces q(x_t | x_0) = ∫ q(x_t | x_{t-1}, x_0) q(x_{t-1} | x_0) dx_{t-1} during joint optimization. Without such a mechanism, the variational objective may optimize an ill-posed target, so that any observed improvement cannot be attributed to better target matching by the factorized reverse process. This issue is load-bearing for the central claim.
minor comments (1)
  1. [Abstract] The abstract refers to 'various benchmarks' without naming the datasets or tasks; adding this information would allow readers to assess the breadth of the empirical support.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive review and for identifying a key aspect of our non-Markovian formulation that requires clarification. We address the major comment below.

read point-by-point responses

  1. Referee: The non-Markovian formulation defines learnable marginal and posterior distributions whose consistency is required for the target distribution to be well-defined. The manuscript does not describe an explicit consistency constraint, reparameterization, or regularization term that enforces q(x_t | x_0) = ∫ q(x_t | x_{t-1}, x_0) q(x_{t-1} | x_0) dx_{t-1} during joint optimization. Without such a mechanism, the variational objective may optimize an ill-posed target, so that any observed improvement cannot be attributed to better target matching by the factorized reverse process. This issue is load-bearing for the central claim.

    Authors: We agree that consistency between the learned marginal q(x_t | x_0) and posterior q(x_{t-1} | x_t, x_0) is essential for the target distribution to be well-defined under the non-Markovian forward process. The current manuscript does not explicitly describe a consistency constraint, reparameterization, or regularization term enforcing the marginalization condition. This omission leaves open the possibility that the variational objective optimizes an ill-posed target, which would weaken attribution of gains to improved target matching by the factorized reverse process. To resolve this, we will revise the Methods section to add a dedicated paragraph and accompanying equations that specify how consistency is maintained. In the revised version we will introduce a lightweight consistency regularization term (estimated via Monte Carlo sampling over the learned posterior) that is added to the standard variational objective with a small fixed coefficient; we will also describe the parameterization chosen for the marginal and posterior so that the integral relation holds by construction wherever possible. We will report an ablation confirming that removing this term degrades performance, thereby supporting that the observed improvements stem from a well-defined target. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation introduces independent learnable components

full rationale

The paper introduces newly learnable non-Markovian marginal and posterior distributions for the forward process, optimized jointly with the reverse model under the standard variational objective. This formulation does not reduce by construction to any pre-fitted quantity or prior result, as the learnable forward objects are defined and trained from scratch rather than derived from existing parameters. Experimental comparisons use the same reverse parameterization against conventional discrete diffusion baselines, providing external validation. No load-bearing self-citations, uniqueness theorems from the authors, or ansatzes smuggled via prior work are required for the central claim, making the derivation self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The method rests on the standard variational lower bound for diffusion models plus the new assumption that jointly optimizing forward and reverse parameters will produce a useful non-Markovian schedule.

free parameters (1)
  • parameters of learnable marginal and posterior distributions
    These are optimized end-to-end from data rather than preset.
axioms (1)
  • domain assumption The variational objective remains valid when both forward and reverse processes are parameterized and learned jointly.
    Standard in diffusion literature but extended to a learnable forward process.

pith-pipeline@v0.9.0 · 5716 in / 1190 out tokens · 38952 ms · 2026-05-20T00:21:42.134831+00:00 · methodology

discussion (0)

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Reference graph

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