# Non-Denoising Forward-Time Diffusions

arXiv: https://arxiv.org/abs/2312.14589 · HTML: https://mlsanity.com/paper/2312.14589/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 7 of 7)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Solving Schr"odinger Bridges via Maximum Likelihood](https://mlsanity.com/paper/2106.02081/) (2021)
- [Deep Generative Learning via Schr"odinger Bridge](https://mlsanity.com/paper/2106.10410/) (2021)
- [Simulation of multivariate diffusion bridge](https://mlsanity.com/paper/1405.7728/) (2014)

## Built on by (most cited first, 30 of 77)

- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [SANA-Sprint: One-Step Diffusion with Continuous-Time Consistency Distillation](https://mlsanity.com/paper/2503.09641/) (2025)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [Advantage Weighted Matching: Aligning RL with Pretraining in Diffusion Models](https://mlsanity.com/paper/2509.25050/) (2025)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [Any-Order Flexible Length Masked Diffusion](https://mlsanity.com/paper/2509.01025/) (2025)
- [Target Score Matching](https://mlsanity.com/paper/2402.08667/) (2024)
- [LBM: Latent Bridge Matching for Fast Image-to-Image Translation](https://mlsanity.com/paper/2503.07535/) (2025)
- [Efficient Diffusion Models: A Survey](https://mlsanity.com/paper/2502.06805/) (2025)
- [Simple ReFlow: Improved Techniques for Fast Flow Models](https://mlsanity.com/paper/2410.07815/) (2024)
- [Continuous Diffusion Model for Language Modeling](https://mlsanity.com/paper/2502.11564/) (2025)
- [Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling](https://mlsanity.com/paper/2410.07974/) (2024)
- [Consistency Diffusion Bridge Models](https://mlsanity.com/paper/2410.22637/) (2024)
- [On the Edge of Memorization in Diffusion Models](https://mlsanity.com/paper/2508.17689/) (2025)
- [Discrete Diffusion Schr"odinger Bridge Matching for Graph Transformation](https://mlsanity.com/paper/2410.01500/) (2024)
- [UniGEM: A Unified Approach to Generation and Property Prediction for Molecules](https://mlsanity.com/paper/2410.10516/) (2024)
- [Adjoint Schr"odinger Bridge Sampler](https://mlsanity.com/paper/2506.22565/) (2025)
- [Curly Flow Matching for Learning Non-gradient Field Dynamics](https://mlsanity.com/paper/2510.26645/) (2025)
- [FrameBridge: Improving Image-to-Video Generation with Bridge Models](https://mlsanity.com/paper/2410.15371/) (2024)
- [Re-Dock: Towards Flexible and Realistic Molecular Docking with Diffusion Bridge](https://mlsanity.com/paper/2402.11459/) (2024)
- [Stochastic Optimal Control for Diffusion Bridges in Function Spaces](https://mlsanity.com/paper/2405.20630/) (2024)
- [Theoretical guarantees in KL for Diffusion Flow Matching](https://mlsanity.com/paper/2409.08311/) (2024)
- [Inverse Bridge Matching Distillation](https://mlsanity.com/paper/2502.01362/) (2025)
- [Flow Map Distillation Without Data](https://mlsanity.com/paper/2511.19428/) (2025)
- [Adversarial Schr"odinger Bridge Matching](https://mlsanity.com/paper/2405.14449/) (2024)
- [Flow Matching with Semidiscrete Couplings](https://mlsanity.com/paper/2509.25519/) (2025)
- [FALCON: Few-step Accurate Likelihoods for Continuous Flows](https://mlsanity.com/paper/2512.09914/) (2025)
- [Generalised Flow Maps for Few-Step Generative Modelling on Riemannian Manifolds](https://mlsanity.com/paper/2510.21608/) (2025)
- [Gumbel-Softmax Flow Matching with Straight-Through Guidance for Controllable Biological Sequence Generation](https://mlsanity.com/paper/2503.17361/) (2025)

## Abstract (arXiv)

The scope of this paper is generative modeling through diffusion processes. An approach falling within this paradigm is the work of Song et al. (2021), which relies on a time-reversal argument to construct a diffusion process targeting the desired data distribution. We show that the time-reversal argument, common to all denoising diffusion probabilistic modeling proposals, is not necessary. We obtain diffusion processes targeting the desired data distribution by taking appropriate mixtures of diffusion bridges. The resulting transport is exact by construction, allows for greater flexibility in choosing the dynamics of the underlying diffusion, and can be approximated by means of a neural network via novel training objectives. We develop a unifying view of the drift adjustments corresponding to our and to time-reversal approaches and make use of this representation to inspect the inner workings of diffusion-based generative models. Finally, we leverage on scalable simulation and inference techniques common in spatial statistics to move beyond fully factorial distributions in the underlying diffusion dynamics. The methodological advances contained in this work contribute toward establishing a general framework for generative modeling based on diffusion processes.