# Stochastic Interpolants via Conditional Dependent Coupling

arXiv: https://arxiv.org/abs/2509.23122 · HTML: https://mlsanity.com/paper/2509.23122/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 54 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 30 of 47)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Autoregressive Model Beats Diffusion: Llama for Scalable Image Generation](https://mlsanity.com/paper/2406.06525/) (2024)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [All are Worth Words: A ViT Backbone for Diffusion Models](https://mlsanity.com/paper/2209.12152/) (2022)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Pyramidal Flow Matching for Efficient Video Generative Modeling](https://mlsanity.com/paper/2410.05954/) (2024)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)

## Built on by (most cited first, 7 of 7)

- [Not All Directions Matter: Towards Structured and Task-Aware Low-Rank Model Adaptation](https://mlsanity.com/paper/2603.14228/) (2026)
- [Learning Straight Flows: Variational Flow Matching for Efficient Generation](https://mlsanity.com/paper/2511.17583/) (2025)
- [Self-Supervised Visual Prompting for Cross-Domain Road Damage Detection](https://mlsanity.com/paper/2511.12410/) (2025)
- [Diffusion Subgoal Planning for Long-Horizon Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2609.34575/) (2026)
- [Transition Flow Matching](https://mlsanity.com/paper/2603.15689/) (2026)
- [Drift Flow Matching](https://mlsanity.com/paper/2605.17244/) (2026)
- [Posterior Flow Matching](https://mlsanity.com/paper/2610.13994/) (2026)

## Abstract (arXiv)

Existing image generation models face critical challenges regarding the trade-off between computation and fidelity. Specifically, models relying on a pretrained Variational Autoencoder (VAE) suffer from information loss, limited detail, and the inability to support end-to-end training. In contrast, models operating directly in the pixel space incur prohibitive computational cost. Although cascade models can mitigate computational cost, stage-wise separation prevents effective end-to-end optimization, hampers knowledge sharing, and often results in inaccurate distribution learning within each stage. To address these challenges, we introduce a unified multistage generative framework based on our proposed Conditional Dependent Coupling strategy. It decomposes the generative process into interpolant trajectories at multiple stages, ensuring accurate distribution learning while enabling end-to-end optimization. Importantly, the entire process is modeled as a single unified Diffusion Transformer, eliminating the need for disjoint modules and also enabling knowledge sharing. Extensive experiments demonstrate that our method achieves both high fidelity and efficiency across multiple resolutions.