Retrieval-Augmented Diffusion Modeling for Stochastic Discount Factor Portfolios

Kelvin J. L. Koa; Xinyang Li; Ke-Wei Huang

cs.LGSep 28, 2026

Retrieval-Augmented Diffusion Modeling for Stochastic Discount Factor Portfolios

Authors: Kelvin J. L. Koa, Xinyang Li, Ke-Wei Huang

Organizations: National University of Singapore Asian Institute of Digital Finance

Abstract

In this work, we study portfolio optimization under the stochastic discount factor (SDF) framework by learning market state representations that capture the underlying risk structures of financial data. This is challenging due to several factors: financial markets exhibit non-stationary dynamics with shifting regimes, multimodal inputs such as price and news data often contain stochastic noise, and existing diffusion-based approaches, while effective for modeling stochastic dynamics, rely on assumptions such as isotropic Gaussian noise that fail to capture the state-dependent nature of financial uncertainty. To address these challenges, we introduce RADAR, a retrieval-augmented diffusion framework that learns market representations by conditioning on similar historical regimes. RADAR leverages retrieval to construct context-dependent noise distributions, applies conditional diffusion to denoise multimodal representations, and initializes the diffusion process using empirical statistics to reflect state-dependent uncertainty. Experiments show that RADAR achieves state-of-the-art performance on key risk-adjusted metrics while producing economically meaningful signals on asset returns and correlations.

Figures & tables

Panel of Figure 1 — Figure 1 : Comparison of forecasting and SDF objectives, and the impact of noisy representations.

Figure 2 : Overview of radar , which learns a clean market state representation for SDF estimation.

Figure 3 : The radar framework. The price and text embeddings, noisy market representation and retrieved contextual noise are used in the diffusion process to obtain the clean market representation.

Benchmarks
Model	Sharpe ( $\uparrow$ )	Sortino ( $\uparrow$ )	Calmar ( $\uparrow$ )	CumRet ( $\uparrow$ )	AnnRet ( $\uparrow$ )	MaxDD ( $\downarrow$ )	Vol ( $\downarrow$ )
S&P 500	0.513	0.576	0.244	0.487	0.083	0.339	0.191
Equal Weight [ 6 ]	0.795	0.873	0.393	1.005	0.149	0.380	0.200
Forecasting
HAN [ 20 ]	0.705	0.816	0.355	0.892	0.123	0.347	0.191
StockNet [ 52 ]	0.780	0.899	0.387	1.218	0.156	0.404	0.216

Table 1 : Performance comparison. The best baselines are underlined, and the best results are bolded.

Data
Model	Sharpe ( $\uparrow$ )	Sortino ( $\uparrow$ )	Calmar ( $\uparrow$ )	CumRet ( $\uparrow$ )	AnnRet ( $\uparrow$ )	MaxDD ( $\downarrow$ )	Vol ( $\downarrow$ )
w/o News	0.650	0.821	0.304	1.229	0.174	0.573	0.332
w/o Price	0.797	0.878	0.395	1.003	0.149	0.377	0.200
Components
SDF (baseline)	0.505	0.690	0.313	0.211	0.039	0.125	0.083
+ Embeddings	0.859	0.959	0.429	1.138	0.164	0.383	0.201

Table 2 : Ablation study across different data and component variations of the radar framework.

Panel of Figure 4 — Figure 4 : Effect of different top- $K$ values on performance and stability across random seeds.

Figure 5 : Embedding Similarity vs Returns Correlation. Reported values are aggregated over 5 rolling windows.

Figure 6 : Quintile Portfolio NAV by Asset Scoring.

Figure 7 : Performance across different input length

L

and rebalancing horizon

H

. Each pair shares its

y

-axis. S&P 500 and Equal Weight do not depend on

L

and

H

, and are drawn as reference lines.

Domain	No Diff.	Gaussian	radar
Agriculture	2.328	2.375	2.240
Climate	0.484	0.464	0.464
Energy	1.753	0.540	0.517
Environment	0.931	0.946	0.928
Health (AFR)	2.413	4.203	1.635
Health (US)	1.007	0.956	0.821

Table 3: Generalizability on different domains.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Baseline	Monthly $p$	HAC $p$	DM $p$	LW $p$
Equal Weight	0.0016***	0.0015***	0.0015***	0.0079***
HAN	0.0015***	0.0016***	0.0016***	0.0105**
StockNet	0.0021***	0.0030***	0.0030***	0.0137**
iTransformer	0.0041***	0.0042***	0.0041***	0.0402**
NGAT	0.0011***	0.0013***	0.0012***	0.0081***
RATD	0.0003***	0.0005***	0.0005***	0.0018***

Appendix

Table 4: Pooled significance tests comparing radar against baselines. The reported results are taken from observations across five random seeds. Significance levels:

{}^{***}p<0.01

{}^{**}p<0.05

{}^{*}p<0.1

Baseline	Bootstrap $p$	Boot $\Delta$ Sharpe $p$	Fisher HAC $p$	Fisher Monthly $p$
Equal Weight	0.0023***	0.0153**	0.0012***	0.0020***
HAN	0.0019***	0.0129**	0.0008***	0.0013***
StockNet	0.0045***	0.0236**	0.0041***	0.0064***
iTransformer	0.0044***	0.0314**	0.0024***	0.0036***
NGAT	0.0020***	0.0126**	0.0007***	0.0011***
RATD	0.0012***	0.0044***	0.0005***	0.0010***

Appendix

Table 5: Robustness statistical significance. Significance levels:

{}^{***}p<0.01

{}^{**}p<0.05

{}^{*}p<0.1

Panel of Figure 8 — Figure 8 : Performance comparison across different volatility groups. radar consistently achieves higher risk-adjusted performance while maintaining competitive returns across all volatility segments.

Figure 9 : Sharpe ratio across sector groups.

Figure 10 : Annualized returns across sector groups.

Model	$\alpha$	$t$ -stat	$p$ -value	$\beta$	$R^{2}$
Equal Weight	4.78%***	2.712	0.003	1.030	0.957
BSV	6.60%*	1.614	0.053	1.248	0.849
DKKM	4.10%***	2.403	0.008	1.019	0.960
MLP	4.86%**	1.864	0.031	0.893	0.897
LinAttn	7.13%**	2.208	0.014	1.051	0.859
SDF	5.34%*	1.352	0.088	0.983	0.816

Appendix

Table 6: CAPM regression results. Significance levels:

{}^{***}p<0.01

{}^{**}p<0.05

{}^{*}p<0.1

Model	$\alpha$	$t$ -stat	$p$ -value	$\beta_{m}$	$\beta_{SMB}$	$\beta_{HML}$	$R^{2}$
Equal Weight	4.63%***	3.233	0.001	0.999	0.079	0.159	0.975
BSV	8.73%***	2.833	0.002	1.192	0.402	0.327	0.918
DKKM	3.88%***	2.735	0.003	0.988	0.042	0.156	0.974
MLP	2.30%	0.870	0.192	0.892	-0.079	-0.064	0.896
LinAttn	8.05%***	2.448	0.007	1.007	0.134	0.245	0.889
SDF	7.42%**	2.002	0.023	0.927	0.108	0.347	0.863

Appendix

Table 7: Fama–French regression results. Significance levels:

{}^{***}p<0.01

{}^{**}p<0.05

{}^{*}p<0.1

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