# Time dependent loss reweighting for flow matching and diffusion models is theoretically justified

arXiv: https://arxiv.org/abs/2511.16599 · HTML: https://mlsanity.com/paper/2511.16599/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 12 of 12)

- [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)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Edit Flows: Flow Matching with Edit Operations](https://mlsanity.com/paper/2506.09018/) (2025)
- [Trajectory Flow Matching with Applications to Clinical Time Series Modeling](https://mlsanity.com/paper/2410.21154/) (2024)
- [OneFlow: Concurrent Mixed-Modal and Interleaved Generation with Edit Flows](https://mlsanity.com/paper/2510.03506/) (2025)
- [Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions](https://mlsanity.com/paper/2511.09465/) (2025)

## Built on by (most cited first, 2 of 2)

- [Preconditioned Flow Matching](https://mlsanity.com/paper/2603.02337/) (2026)
- [Latent Process Generator Matching](https://mlsanity.com/paper/2605.20547/) (2026)

## Abstract (arXiv)

This brief note clarifies that, in Generator Matching (which subsumes a large family of flow matching and diffusion models over continuous, manifold, and discrete spaces), both the Bregman divergence loss and the linear parameterization of the generator can depend on both the current state Xt and the time t, and we show that the expectation over time in the loss can be taken with respect to a broad class of time distributions. We also show this for Edit Flows, which falls outside of Generator Matching. That the loss can depend on t clarifies that time-dependent loss weighting schemes, often used in practice to stabilize training, are theoretically justified when the specific flow or diffusion scheme is a special case of Generator Matching (or Edit Flows). It also often simplifies the construction of X1-predictor schemes, which are sometimes preferred for model-related reasons. We show examples that rely upon the dependence of linear parameterizations, and of the Bregman divergence loss, on t and Xt.