BiCFlow-MER：通过条件传输协调判别式与生成式多模态情感识别

# BiCFlow-MER: Orchestrating Discriminative and Generative Multimodal Emotion Recognition via Conditional Transport
Source: [https://arxiv.org/html/2609.27615](https://arxiv.org/html/2609.27615)
###### Abstract

In multimodal emotion recognition \(MER\), human affective states are inferred by integrating complementary cues from multiple modalities\. In audio\-text MER, affective cues are often entangled with speaker style and lexical content, while cross\-modal disagreement further complicates how the evidence should be integrated\. Under conventional discriminative fusion, multimodal evidence is compressed into a terminal prediction, with modality\-specific cues and conflict information insufficiently preserved\. In large generative affective models, by contrast, affective reasoning is typically embedded in language decoding, leaving emotion evidence implicit and difficult to verify in a structured space\. To address these limitations, BiCFlow\-MER \(Bidirectional Conditional Flow for Multimodal Emotion Recognition\) is proposed as a conditional\-flow framework in which audio\-text MER is formulated as generative evidence transport within a structured emotion space\. Within BiCFlow\-MER, emotion\-oriented evidence is disentangled from speaker\-style and lexical\-content factors to construct a conflict\-aware affective condition\. Guided by this condition, each utterance is transported to an explicit emotion\-space endpoint through a bidirectional rectified flow\. Candidate emotions are jointly scored through adaptive prototype\-cloud geometry of the transported endpoint and backward compatibility with the condition\-dependent start region, enabling conflict\-aware recognition\. BiCFlow\-MER achieves the best reported results among all compared methods across IEMOCAP, MELD, and the zero\-shot CASE benchmark\. By orchestrating discriminative recognition and generative evidence modeling through conditional transport, BiCFlow\-MER defines a new MER paradigm\.

OPPO Research Institute

\{wangyanbing1, wangshenyue, yuchunyang\}@oppo\.com

## Introduction

MER aims to infer a speaker’s affective state from behavioral signals such as speech, transcripts, and visual cues\([Heredia et al\. 2022](https://arxiv.org/html/2609.27615#bib.bib5);[Peña et al\. 2023](https://arxiv.org/html/2609.27615#bib.bib6)\)\. Beyond its scientific role in affective computing, MER supports customer\-experience analytics, human\-computer interaction, intelligent assistants, and mental\-health applications\. Industry demand reflects this direction: a MarketsandMarkets report estimates the global emotion detection and recognition market at $26\.76B in 2025 and $43\.29B by 2031, with an 8\.35% CAGR from 2024\-2031\. The report also identifies customer\-experience analytics as the largest 2031 application segment and multimodal data fusion as the fastest\-growing technology direction\. These trends create a practical requirement for MER: emotion must be recognized reliably from signals already available in real\-world interfaces, without introducing substantial sensing cost or privacy burden\. Audio and transcripts meet this requirement better than visual streams, which often depend on camera availability, bandwidth, lighting, and device placement\([Ghosh et al\. 2022](https://arxiv.org/html/2609.27615#bib.bib17);[Lin and Wang 2023](https://arxiv.org/html/2609.27615#bib.bib2);[Wang et al\. 2025](https://arxiv.org/html/2609.27615#bib.bib18)\)\. Yet real\-world audio and text do not provide clean or consistently aligned emotion evidence: vocal affect is entangled with speaker style, lexical affect with semantic content, and tone may contradict words\. Most audio\-text MER systems nevertheless fuse these signals and map the fused representation directly to an emotion label\([Tsai et al\. 2019](https://arxiv.org/html/2609.27615#bib.bib26);[Wang et al\. 2024](https://arxiv.org/html/2609.27615#bib.bib3);[Fan et al\. 2025](https://arxiv.org/html/2609.27615#bib.bib4);[Wang et al\. 2025](https://arxiv.org/html/2609.27615#bib.bib18)\)\. This terminal decision leaves three evidence\-level questions only indirectly modeled: which part of the signal reflects emotion rather than speaker style or lexical content; how audio\-text disagreement should modulate fusion; and whether a candidate emotion remains compatible with the observed evidence\([Zhang et al\. 2024](https://arxiv.org/html/2609.27615#bib.bib8);[Liu and Wang 2026](https://arxiv.org/html/2609.27615#bib.bib10);[Huang et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib40)\)\.

Generative modeling offers one way to make affective evidence formation more explicit\. Diffusion and rectified\-flow models connect simple priors to structured data distributions through continuous trajectories\([Liu et al\. 2022](https://arxiv.org/html/2609.27615#bib.bib7);[Peebles and Xie 2023](https://arxiv.org/html/2609.27615#bib.bib29)\), while large language model \(LLM\) and multimodal large language model \(MLLM\) affective systems popularize intermediate reasoning and explanatory affect analysis\([Xu et al\. 2024](https://arxiv.org/html/2609.27615#bib.bib9);[Li et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib15);[Rha et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib16)\)\. For audio\-text MER, however, large generative affective systems often couple recognition to token decoding, model scale, prompt design, or additional visual and conversational context\. The relevant question is therefore how to obtain a compact generative evidence object that can be checked against the original speech and language signals\.

This paper introducesBiCFlow\-MER, a conditional flow framework for audio\-text MER\. BiCFlow\-MER first builds an affective condition𝐜\\mathbf\{c\}by separating emotion\-oriented evidence from speaker style and lexical content and by using audio\-text conflict to modulate fusion\. Conditional Trajectory Bidirectional Rectified Flow \(CT\-BiRF\) then transports a condition\-dependent start point toward an emotion\-space endpoint𝐞^1\\hat\{\\mathbf\{e\}\}\_\{1\}, making the generated endpoint an explicit evidence object for recognition\. Adaptive Geometric Classification Head \(A\-GCH\) and Bidirectional Generative Decision \(BGD\) evaluate this endpoint through forward prototype\-cloud geometry and backward compatibility scoring\. The resulting pipeline turns audio\-text evidence into a transportable endpoint and then verifies the endpoint geometrically, linking evidence construction, conditional flow, and class\-level decision checking in a single recognition process\. The main contributions are organized at the paradigm, module, and empirical levels:

- •Generative\-decision paradigm\.BiCFlow\-MER replaces terminal fusion\-to\-label mapping with conditional transport to an explicit emotion\-space endpoint followed by forward geometric scoring and backward compatibility scoring\.
- •Evidence construction and scoring modules\.Emotion\-oriented factorization and ECA construct a conflict\-aware affective condition, while CT\-BiRF, A\-GCH, and BGD perform endpoint transport and bidirectional class scoring\.
- •Empirical validation\.Experiments on IEMOCAP, MELD, and zero\-shot CASE, together with controlled variants, evaluate standard recognition, conflict transfer, and the roles of the main components\.

## Related Work

#### Discriminative audio\-text MER\.

Most utterance\-level MER systems encode speech and language with pretrained backbones, align or attend across modalities, and map the fused representation to emotion labels\([Tsai et al\. 2019](https://arxiv.org/html/2609.27615#bib.bib26);[Ghosh et al\. 2022](https://arxiv.org/html/2609.27615#bib.bib17);[Wang et al\. 2025](https://arxiv.org/html/2609.27615#bib.bib18)\)\. Recent variants improve this pipeline with modality\-specific self\-supervision, empirical fusion design, cross\-space synergy, incomplete\-modality prompting, and consistency\-aware learning\([Yu et al\. 2021](https://arxiv.org/html/2609.27615#bib.bib27);[Wu et al\. 2023](https://arxiv.org/html/2609.27615#bib.bib19);[Lyu et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib11);[He et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib13);[Yin et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib14)\)\. These methods improve representation learning but retain terminal classification, leaving evidence formation and class compatibility implicit\. BiCFlow\-MER instead transports and geometrically verifies the fused evidence\.

#### Affective evidence factorization\.

Another line separates emotion from speaker style, lexical content, or other nuisance factors through factorized subspaces, variational bottlenecks, and Contrastive Log\-ratio Upper Bound \(CLUB\)\-based mutual\-information control\([Liu and Wang 2026](https://arxiv.org/html/2609.27615#bib.bib10);[Kingma and Welling 2013](https://arxiv.org/html/2609.27615#bib.bib30);[Cheng et al\. 2020](https://arxiv.org/html/2609.27615#bib.bib24)\)\. Factorization improves affective representations but stops before post\-fusion evidence organization and verification\. BiCFlow\-MER uses emotion\-oriented factors to construct the transport condition\.

#### Generative modeling and conditional transport\.

Generative affective systems, including LLM and MLLM\-based methods, have introduced richer intermediate structures such as emotional descriptions and rationale\-based affect analysis\([Wu et al\. 2025](https://arxiv.org/html/2609.27615#bib.bib12);[Li et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib15);[Rha et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib16)\)\. Continuous generative models provide another route: rectified flow learns transport trajectories from simple priors to structured data distributions\([Liu et al\. 2022](https://arxiv.org/html/2609.27615#bib.bib7)\), and transformer velocity fields extend this formulation\([Peebles and Xie 2023](https://arxiv.org/html/2609.27615#bib.bib29)\)\. Recent speech\-emotion and ambiguity\-aware methods also explore distributional or transport\-inspired supervision\([Wang et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib20);[Wu et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib31)\)\. These methods produce textual explanations or distributional supervision but do not construct and verify an audio\-text emotion endpoint\. BiCFlow\-MER generates a condition\-dependent endpoint\.

#### Prototype geometry and verification\.

Distance\- and prototype\-based decisions are well established in metric learning\([Schroff et al\. 2015](https://arxiv.org/html/2609.27615#bib.bib28)\)\. Prototype scoring measures class proximity but not compatibility with the condition\-dependent start region\. BiCFlow\-MER combines adaptive prototype clouds with backward class\-to\-condition compatibility scoring\.

## Method

### Overview and Problem Formulation

Given paired utterance\-level audio𝐱a\\mathbf\{x\}\_\{a\}and transcript𝐱t\\mathbf\{x\}\_\{t\}, the goal is to predict emotion labely∈\{1,…,K\}y\\in\\\{1,\\ldots,K\\\}\. BiCFlow\-MER organizes recognition as evidence construction, conditional transport, and bidirectional geometric scoring\. It maps the inputs to an affective condition𝐜∈ℝdc\\mathbf\{c\}\\in\\mathbb\{R\}^\{d\_\{c\}\}, transports a condition\-dependent start through add\-dimensional emotion flow spaceℰ\\mathcal\{E\}\(d=64d\{=\}64\), and evaluates the generated endpoint𝐞^1∈ℰ\\hat\{\\mathbf\{e\}\}\_\{1\}\\in\\mathcal\{E\}in both forward and backward directions:

\(𝐱a,𝐱t\)\\displaystyle\(\\mathbf\{x\}\_\{a\},\\mathbf\{x\}\_\{t\}\)→evidence𝐜→transport𝐞^1,\\displaystyle\\xrightarrow\{\\text\{evidence\}\}\\mathbf\{c\}\\xrightarrow\{\\text\{transport\}\}\\hat\{\\mathbf\{e\}\}\_\{1\},\(1\)\(𝐞^1,𝐜\)\\displaystyle\(\\hat\{\\mathbf\{e\}\}\_\{1\},\\mathbf\{c\}\)→geometric scoring\{ℓkfwd,ℓkbwd\}k=1K⟶y^\.\\displaystyle\\xrightarrow\{\\text\{geometric scoring\}\}\\\{\\ell\_\{k\}^\{\\mathrm\{fwd\}\},\\ell\_\{k\}^\{\\mathrm\{bwd\}\}\\\}\_\{k=1\}^\{K\}\\longrightarrow\\hat\{y\}\.Figure[1](https://arxiv.org/html/2609.27615#Sx3.F1)summarizes the architecture\. For modalitym∈\{a,t\}m\\in\\\{a,t\\\},𝐳Em\\mathbf\{z\}\_\{E\}^\{m\},𝐳Sm\\mathbf\{z\}\_\{S\}^\{m\}, and𝐳Cm\\mathbf\{z\}\_\{C\}^\{m\}denote emotion, style, and content factors;𝐞t\\mathbf\{e\}\_\{t\}is the flow state att∈\[0,1\]t\\in\[0,1\]; and\(𝝁k,𝚺k\)\(\\boldsymbol\{\\mu\}\_\{k\},\\boldsymbol\{\\Sigma\}\_\{k\}\)parameterizes the adaptive prototype cloud of classkk\. The forward score tests whether𝐞^1\\hat\{\\mathbf\{e\}\}\_\{1\}belongs to a class cloud, while the backward score tests whether that class hypothesis reconstructs the condition\-dependent start region\.

![Refer to caption](https://arxiv.org/html/2609.27615v1/Figures/pipeline.png)Figure 1:BiCFlow\-MER pipeline\. Encoder features and CGD\-IB emotion factors are combined through multi\-scale fusion and ECA to form the affective condition𝐜\\mathbf\{c\}\. CT\-BiRF transports a condition\-dependent start𝐞0=m⁡\(𝐜\)\+𝝈0⊙𝜺0\\mathbf\{e\}\_\{0\}=m\(\\mathbf\{c\}\)\+\\boldsymbol\{\\sigma\}\_\{0\}\\odot\\boldsymbol\{\\varepsilon\}\_\{0\}to the endpoint𝐞^1\\hat\{\\mathbf\{e\}\}\_\{1\}, which A\-GCH scores against adaptive prototype clouds\. BGD maps each class prototype mean𝝁k\\boldsymbol\{\\mu\}\_\{k\}back to a reconstructed start𝐞^0\(k\)\\hat\{\\mathbf\{e\}\}\_\{0\}^\{\(k\)\}and compares it with the prior centerm⁡\(𝐜\)m\(\\mathbf\{c\}\)\. A single reconstruction and the displayed class clouds are schematic\.
### Affective Evidence Factorization

BiCFlow\-MER first separates emotion\-oriented evidence from style and content variation in each modality\. In the IEMOCAP/MELD configuration, audio and text are encoded by WavLM\-Large and DeBERTa\-v3 with low\-rank adaptation \(LoRA\) fine\-tuning\([Chen et al\. 2022](https://arxiv.org/html/2609.27615#bib.bib22);[He et al\. 2020](https://arxiv.org/html/2609.27615#bib.bib23);[Hu et al\. 2022](https://arxiv.org/html/2609.27615#bib.bib25)\):

𝐡m=fm​\(𝐱m\),m∈\{a,t\}\.\\mathbf\{h\}\_\{m\}=f\_\{m\}\(\\mathbf\{x\}\_\{m\}\),\\quad m\\in\\\{a,t\\\}\.\(2\)The Causal Generative Disentanglement with an Information Bottleneck \(CGD\-IB\) block mask\-pools each encoded sequence and uses threedzd\_\{z\}\-dimensional variational heads forr∈\{E,S,C\}r\\in\\\{E,S,C\\\}:

qϕ​\(𝐳rm∣𝐡m\)\\displaystyle q\_\{\\phi\}\(\\mathbf\{z\}\_\{r\}^\{m\}\\mid\\mathbf\{h\}\_\{m\}\)=𝒩⁡\(𝝁rm,diag⁡\(\(𝝈rm\)2\)\),\\displaystyle=\\mathcal\{N\}\\\!\\left\(\\boldsymbol\{\\mu\}\_\{r\}^\{m\},\\operatorname\{diag\}\(\(\\boldsymbol\{\\sigma\}\_\{r\}^\{m\}\)^\{2\}\)\\right\),\(3\)𝐳rm\\displaystyle\\mathbf\{z\}\_\{r\}^\{m\}=𝝁rm\+𝝈rm⊙𝜺rm,𝜺rm∼𝒩\(𝟎,𝐈dz\)\.\\displaystyle=\\boldsymbol\{\\mu\}\_\{r\}^\{m\}\+\\boldsymbol\{\\sigma\}\_\{r\}^\{m\}\\odot\\boldsymbol\{\\varepsilon\}\_\{r\}^\{m\},\\quad\\boldsymbol\{\\varepsilon\}\_\{r\}^\{m\}\\sim\\mathcal\{N\}\(\\mathbf\{0\},\\mathbf\{I\}\_\{d\_\{z\}\}\)\.Table[1](https://arxiv.org/html/2609.27615#Sx3.T1)summarizes the contract imposed on these factors\.

Table 1:Roles of the modality\-specific factors produced by CGD\-IB\.The active factorization objective is

ℒCGD=ℒreca\+ℒrect\+βIB​ℒKL\+λcf​ℒcf\+λE​ℒE\.\\mathcal\{L\}\_\{\\mathrm\{CGD\}\}=\\mathcal\{L\}\_\{\\mathrm\{rec\}\}^\{a\}\+\\mathcal\{L\}\_\{\\mathrm\{rec\}\}^\{t\}\+\\beta\_\{\\mathrm\{IB\}\}\\mathcal\{L\}\_\{\\mathrm\{KL\}\}\+\\lambda\_\{\\mathrm\{cf\}\}\\mathcal\{L\}\_\{\\mathrm\{cf\}\}\+\\lambda\_\{E\}\\mathcal\{L\}\_\{E\}\.\(4\)ℒreca\\mathcal\{L\}\_\{\\mathrm\{rec\}\}^\{a\}andℒrect\\mathcal\{L\}\_\{\\mathrm\{rec\}\}^\{t\}reconstruct the representations supplied to their respective audio/acoustic and text/semantic branches from the three branch factors, andℒKL\\mathcal\{L\}\_\{\\mathrm\{KL\}\}regularizes all variational posteriors\. Forℒcf\\mathcal\{L\}\_\{\\mathrm\{cf\}\}, style factors are exchanged across different\-label minibatch samples, the resulting features are decoded, and their emotion prediction is constrained to retain the source label\.ℒE\\mathcal\{L\}\_\{E\}directly constrains each emotion factor to preserve label\-relevant semantics during factorization\.

The factor\-level classifiers optimized byℒE\\mathcal\{L\}\_\{E\}produce modality\-specific class probabilities from𝐳Ea\\mathbf\{z\}\_\{E\}^\{a\}and𝐳Et\\mathbf\{z\}\_\{E\}^\{t\}\. Letpmmaxp\_\{m\}^\{\\max\}be the maximum class probability of the factor\-level classifier for modalitymm\. From Stage II\.a onward, modality dropout\([Wu et al\. 2023](https://arxiv.org/html/2609.27615#bib.bib19)\)removes the corresponding factor with probability

pdropm=p02​pmmax\.p\_\{\\mathrm\{drop\}\}^\{m\}=\\frac\{p\_\{0\}\}\{2\}\\,p\_\{m\}^\{\\max\}\.\(5\)With base dropout ratep0=0\.2p\_\{0\}\{=\}0\.2, at most one modality is dropped per sample, and higherpmmaxp\_\{m\}^\{\\max\}increases its masking probability\. Only𝐳Em\\mathbf\{z\}\_\{E\}^\{m\}is routed to downstream condition construction; the dashed𝐳Sm\\mathbf\{z\}\_\{S\}^\{m\}and𝐳Cm\\mathbf\{z\}\_\{C\}^\{m\}factors in Figure[1](https://arxiv.org/html/2609.27615#Sx3.F1)remain within CGD\-IB for reconstruction and regularization\.

### Conflict\-Aware Condition Construction

The encoded sequences and the two emotion factors are then combined into the transport condition𝐜\\mathbf\{c\}\.

#### Multi\-scale fusion\.

A multi\-scale latent fusion bottleneck \(MS\-LFB\) projects the audio and text encoder sequences into a shared space and concatenates them along the temporal dimension\. Three parallel paths extract global summaries through learned\-query attention, local salient evidence through Gumbel Top\-KKselection, and short\-term temporal patterns through one\-dimensional convolutions\. The shared MS\-LFB is evaluated under two complementary modality masks\. For the audio\-specific pass, the text mask and𝐳Et\\mathbf\{z\}\_\{E\}^\{t\}are set to zero; for the text\-specific pass, the audio mask and𝐳Ea\\mathbf\{z\}\_\{E\}^\{a\}are set to zero\. Each multi\-scale summary is concatenated with its retained emotion factor and projected by the fusion MLP, producing𝐜afuse,𝐜tfuse∈ℝdf\\mathbf\{c\}\_\{a\}^\{\\mathrm\{fuse\}\},\\mathbf\{c\}\_\{t\}^\{\\mathrm\{fuse\}\}\\in\\mathbb\{R\}^\{d\_\{f\}\}\. These two masked passes correspond to the two MS\-LFB branches in Figure[1](https://arxiv.org/html/2609.27615#Sx3.F1)\.

#### Conflict\-conditioned fusion\.

The Emotion Conflict Awareness \(ECA\) module assigns an energy to each audio\-text emotion\-factor pair:

Eψ=\\displaystyle E\_\{\\psi\}=\{\}‖pψ​\(𝐳Ea\)−pψ​\(𝐳Et\)‖22\\displaystyle\\bigl\\\|p\_\{\\psi\}\(\\mathbf\{z\}\_\{E\}^\{a\}\)\-p\_\{\\psi\}\(\\mathbf\{z\}\_\{E\}^\{t\}\)\\bigr\\\|\_\{2\}^\{2\}\(6\)\+λcos​\(1−cos⁡\(𝐳Ea,𝐳Et\)\)\\displaystyle\+\\lambda\_\{\\cos\}\\bigl\(1\-\\operatorname\{cos\}\(\\mathbf\{z\}\_\{E\}^\{a\},\\mathbf\{z\}\_\{E\}^\{t\}\)\\bigr\)\+sψ​\(\[𝐳Ea;𝐳Et\]\)\.\\displaystyle\+s\_\{\\psi\}\(\[\\mathbf\{z\}\_\{E\}^\{a\};\\mathbf\{z\}\_\{E\}^\{t\}\]\)\.Here,pψp\_\{\\psi\}is a shared projector,sψs\_\{\\psi\}is a learned scalar pair scorer,λcos=0\.5\\lambda\_\{\\cos\}\{=\}0\.5weights cosine disagreement, andγ=0\.1\\gamma\{=\}0\.1scales the standardized conflict\-energy residual in the fused condition\. After standardization toE~ψ\\widetilde\{E\}\_\{\\psi\}using running statistics accumulated during training and frozen at inference, ECA predicts conflict\-conditioned modality weights and constructs

𝐪\\displaystyle\\mathbf\{q\}=gω​\(\[𝐳Ea;𝐳Et;E~ψ\]\)∈ℝ2,\\displaystyle=g\_\{\\omega\}\(\[\\mathbf\{z\}\_\{E\}^\{a\};\\mathbf\{z\}\_\{E\}^\{t\};\\widetilde\{E\}\_\{\\psi\}\]\)\\in\\mathbb\{R\}^\{2\},\(7\)\(αa,αt\)\\displaystyle\(\\alpha\_\{a\},\\alpha\_\{t\}\)=softmax⁡\(𝐪\),\\displaystyle=\\operatorname\{softmax\}\(\\mathbf\{q\}\),𝐜¯\\displaystyle\\bar\{\\mathbf\{c\}\}=αa​𝐜afuse\+αt​𝐜tfuse\+γ​E~ψ​1df,\\displaystyle=\\alpha\_\{a\}\\mathbf\{c\}\_\{a\}^\{\\mathrm\{fuse\}\}\+\\alpha\_\{t\}\\mathbf\{c\}\_\{t\}^\{\\mathrm\{fuse\}\}\+\\gamma\\widetilde\{E\}\_\{\\psi\}\\,\\mathbf\{1\}\_\{d\_\{f\}\},𝐜\\displaystyle\\mathbf\{c\}=𝐖c​𝐜¯\+𝐛c\.\\displaystyle=\\mathbf\{W\}\_\{c\}\\bar\{\\mathbf\{c\}\}\+\\mathbf\{b\}\_\{c\}\.gωg\_\{\\omega\}is a learned modality\-weight scorer optimized end\-to\-end with the downstream objectives\. ECA uses the hinge\-ranking objectiveℒECA=∑j∈𝒜wj​\[δ\+Eψ\+−Eψ,j−\]\+\\mathcal\{L\}\_\{\\mathrm\{ECA\}\}=\\sum\_\{j\\in\\mathcal\{A\}\}w\_\{j\}\[\\delta\+E\_\{\\psi\}^\{\+\}\-E\_\{\\psi,j\}^\{\-\}\]\_\{\+\}with marginδ=0\.5\\delta\{=\}0\.5, weights\(w1,w2,w3\)=\(0\.3,0\.4,0\.3\)\(w\_\{1\},w\_\{2\},w\_\{3\}\)\{=\}\(0\.3,0\.4,0\.3\), overall weight 0\.1, and a Huber energy regularizer weighted by 0\.001\. Here,Eψ\+E\_\{\\psi\}^\{\+\}is the matched\-pair energy; N1 \(cross\-emotion mismatches\) and N2 \(same\-emotion noncorresponding pairs\) form𝒜=\{1,2\}\\mathcal\{A\}\{=\}\\\{1,2\\\}in Stage II\.a, while Stage II\.b uses𝒜=\{1,2,3\}\\mathcal\{A\}\{=\}\\\{1,2,3\\\}by adding N3 \(independently shuffled pairs\)\.

### CT\-BiRF

CT\-BiRF generates a compact endpoint in the emotion flow spaceℰ\\mathcal\{E\}from the affective condition𝐜\\mathbf\{c\}\. Building on rectified flow\([Liu et al\. 2022](https://arxiv.org/html/2609.27615#bib.bib7)\), it uses forward and backward velocity fields𝐯f\\mathbf\{v\}\_\{f\}and𝐯b\\mathbf\{v\}\_\{b\}with a shared Diffusion Transformer \(DiT\)\-style trunk and direction\-specific blocks and output heads\. The affective condition𝐜\\mathbf\{c\}parameterizes both fields throughout forward transport and backward compatibility scoring\. The two fields model opposite directions along the same conditional path:

𝐯f​\(𝐞t,t,𝐜\)\\displaystyle\\mathbf\{v\}\_\{f\}\(\\mathbf\{e\}\_\{t\},t,\\mathbf\{c\}\)≈𝐞1−𝐞0,\\displaystyle\\approx\\mathbf\{e\}\_\{1\}\-\\mathbf\{e\}\_\{0\},\(8\)𝐯b​\(𝐞t,t,𝐜\)\\displaystyle\\mathbf\{v\}\_\{b\}\(\\mathbf\{e\}\_\{t\},t,\\mathbf\{c\}\)≈𝐞0−𝐞1\.\\displaystyle\\approx\\mathbf\{e\}\_\{0\}\-\\mathbf\{e\}\_\{1\}\.
#### Conditional prior\.

Instead of sampling𝐞0∼𝒩⁡\(𝟎,𝐈d\)\\mathbf\{e\}\_\{0\}\\sim\\mathcal\{N\}\(\\mathbf\{0\},\\mathbf\{I\}\_\{d\}\), the start point is drawn as

𝐞0=m⁡\(𝐜\)\+𝝈0⊙𝜺0,𝜺0∼𝒩⁡\(𝟎,𝐈d\),\\mathbf\{e\}\_\{0\}=m\(\\mathbf\{c\}\)\+\\boldsymbol\{\\sigma\}\_\{0\}\\odot\\boldsymbol\{\\varepsilon\}\_\{0\},\\quad\\boldsymbol\{\\varepsilon\}\_\{0\}\\sim\\mathcal\{N\}\(\\mathbf\{0\},\\mathbf\{I\}\_\{d\}\),\(9\)where an MLP predicts the deterministic centerm⁡\(𝐜\)m\(\\mathbf\{c\}\)and𝝈0\\boldsymbol\{\\sigma\}\_\{0\}is a learned diagonal scale\. Thus,m⁡\(𝐜\)m\(\\mathbf\{c\}\)identifies the condition\-dependent start region, while𝐞0\\mathbf\{e\}\_\{0\}is a stochastic point sampled from that region\.

#### Terminal targets and prototype anchoring\.

The target distribution is estimated from emotion factors rather than generated endpoints\. For each minibatch, the post\-dropout modality factors are averaged and projected intoℰ\\mathcal\{E\}:

𝐫=𝐖p​𝐳¯E,𝐳¯E=12​\(𝐳Ea\+𝐳Et\)\.\\mathbf\{r\}=\\mathbf\{W\}\_\{p\}\\bar\{\\mathbf\{z\}\}\_\{E\},\\qquad\\bar\{\\mathbf\{z\}\}\_\{E\}=\\tfrac\{1\}\{2\}\(\\mathbf\{z\}\_\{E\}^\{a\}\+\\mathbf\{z\}\_\{E\}^\{t\}\)\.\(10\)Detached vectors𝐫\\mathbf\{r\}are stored in a per\-class first\-in\-first\-out \(FIFO\) memory bankℳk\\mathcal\{M\}\_\{k\}with capacity 256\. The bank estimates a mean𝝁k\\boldsymbol\{\\mu\}\_\{k\}and an adaptive diagonal\-plus\-low\-rank covariance

𝚺k=𝐃k\+𝐔k​𝐔k⊤\+αk​v¯​𝐈d,\\boldsymbol\{\\Sigma\}\_\{k\}=\\mathbf\{D\}\_\{k\}\+\\mathbf\{U\}\_\{k\}\\mathbf\{U\}\_\{k\}^\{\\top\}\+\\alpha\_\{k\}\\bar\{v\}\\,\\mathbf\{I\}\_\{d\},\(11\)where𝐃k\\mathbf\{D\}\_\{k\}is the diagonal covariance component,𝐔k​𝐔k⊤\\mathbf\{U\}\_\{k\}\\mathbf\{U\}\_\{k\}^\{\\top\}captures rank\-4 correlations,𝐈d\\mathbf\{I\}\_\{d\}is thedd\-dimensional identity matrix, andv¯\\bar\{v\}is the global mean within\-class variance\. For class countnkn\_\{k\}, shrinkage isαk=min⁡\{0\.1/nk/100,0\.5\}\\alpha\_\{k\}=\\min\\\{0\.1/\\sqrt\{n\_\{k\}/100\},0\.5\\\}\. The terminal target for a sample with labelyyis then drawn from the resulting prototype cloud:

𝐞1∼𝒩⁡\(𝝁y,𝚺y\)\.\\mathbf\{e\}\_\{1\}\\sim\\mathcal\{N\}\(\\boldsymbol\{\\mu\}\_\{y\},\\boldsymbol\{\\Sigma\}\_\{y\}\)\.\(12\)This construction lets the same class clouds define both flow targets and geometric decisions without feeding𝐞^1\\hat\{\\mathbf\{e\}\}\_\{1\}back into their statistics\.

#### Class\-conditioned stochastic interpolation\.

During training, interpolated states are perturbed:

𝐞t\\displaystyle\\mathbf\{e\}\_\{t\}=\(1−t\)​𝐞0\+t​𝐞1\+𝝈⁡\(𝐜,t,y\)⊙𝜺t,\\displaystyle=\(1\-t\)\\mathbf\{e\}\_\{0\}\+t\\mathbf\{e\}\_\{1\}\+\\boldsymbol\{\\sigma\}\(\\mathbf\{c\},t,y\)\\odot\\boldsymbol\{\\varepsilon\}\_\{t\},\(13\)𝟎\\displaystyle\\mathbf\{0\}⪯𝝈⁡\(𝐜,t,y\)⪯σmax​𝟏d\.\\displaystyle\\preceq\\boldsymbol\{\\sigma\}\(\\mathbf\{c\},t,y\)\\preceq\\sigma\_\{\\max\}\\mathbf\{1\}\_\{d\}\.Here,𝜺t∼𝒩⁡\(𝟎,𝐈d\)\\boldsymbol\{\\varepsilon\}\_\{t\}\\sim\\mathcal\{N\}\(\\mathbf\{0\},\\mathbf\{I\}\_\{d\}\),σmax=0\.1\\sigma\_\{\\max\}\{=\}0\.1, and⪯\\preceqdenotes an elementwise bound on the scale predicted from the condition, time, and label\. The perturbation is used as off\-path neighborhood augmentation, while the supervised velocity remains the nominal rectified displacement𝐞1−𝐞0\\mathbf\{e\}\_\{1\}\-\\mathbf\{e\}\_\{0\}\.

#### Bidirectional flow losses\.

Let𝚫=𝐞1−𝐞0\\boldsymbol\{\\Delta\}=\\mathbf\{e\}\_\{1\}\-\\mathbf\{e\}\_\{0\}\. The flow\-matching and bidirectional consistency losses are

ℒrff\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{rf\}\}^\{f\}=𝔼⁡\[κy​‖𝐯f​\(𝐞t,t,𝐜\)−𝚫‖22\],\\displaystyle=\\mathbb\{E\}\\\!\\left\[\\kappa\_\{y\}\\\|\\mathbf\{v\}\_\{f\}\(\\mathbf\{e\}\_\{t\},t,\\mathbf\{c\}\)\-\\boldsymbol\{\\Delta\}\\\|\_\{2\}^\{2\}\\right\],\(14\)ℒrfb\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{rf\}\}^\{b\}=𝔼⁡\[‖𝐯b​\(𝐞t,t,𝐜\)\+𝚫‖22\],\\displaystyle=\\mathbb\{E\}\\\!\\left\[\\\|\\mathbf\{v\}\_\{b\}\(\\mathbf\{e\}\_\{t\},t,\\mathbf\{c\}\)\+\\boldsymbol\{\\Delta\}\\\|\_\{2\}^\{2\}\\right\],ℒbc\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{bc\}\}=𝔼⁡\[‖𝐯f​\(𝐞t,t,𝐜\)\+𝐯b​\(𝐞t,t,𝐜\)‖22\],\\displaystyle=\\mathbb\{E\}\\\!\\left\[\\\|\\mathbf\{v\}\_\{f\}\(\\mathbf\{e\}\_\{t\},t,\\mathbf\{c\}\)\+\\mathbf\{v\}\_\{b\}\(\\mathbf\{e\}\_\{t\},t,\\mathbf\{c\}\)\\\|\_\{2\}^\{2\}\\right\],whereκy=1\+βκ​tr⁡\(𝚺y\)/\(K−1​∑k=1Ktr⁡\(𝚺k\)\)\\kappa\_\{y\}=1\+\\beta\_\{\\kappa\}\\operatorname\{tr\}\(\\boldsymbol\{\\Sigma\}\_\{y\}\)\\big/\\left\(K^\{\-1\}\\sum\_\{k=1\}^\{K\}\\operatorname\{tr\}\(\\boldsymbol\{\\Sigma\}\_\{k\}\)\\right\)weights forward supervision by the normalized trace of the target\-class prototype covariance, withβκ=0\.5\\beta\_\{\\kappa\}\{=\}0\.5\. Both fields are evaluated at the same interpolated state and time, enforcing opposite velocities along the same conditional path\. Terminal prototype inversion is evaluated att=1t=1\. For two independently sampled times on the same conditional path, sharing\(𝐞0,𝐞1,𝐜\)\(\\mathbf\{e\}\_\{0\},\\mathbf\{e\}\_\{1\},\\mathbf\{c\}\)while using independent stochastic perturbations, define

𝐟ti\\displaystyle\\mathbf\{f\}\_\{t\_\{i\}\}=𝐞ti\+\(1−ti\)​𝐯f​\(𝐞ti,ti,𝐜\),\\displaystyle=\\mathbf\{e\}\_\{t\_\{i\}\}\+\(1\-t\_\{i\}\)\\mathbf\{v\}\_\{f\}\(\\mathbf\{e\}\_\{t\_\{i\}\},t\_\{i\},\\mathbf\{c\}\),\(15\)ℒct\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{ct\}\}=𝔼​‖𝐟t1−𝐟t2‖22\.\\displaystyle=\\mathbb\{E\}\\\|\\mathbf\{f\}\_\{t\_\{1\}\}\-\\mathbf\{f\}\_\{t\_\{2\}\}\\\|\_\{2\}^\{2\}\.This term aligns extrapolated endpoints; relative to unit\-weight forward matching, backward matching, bidirectional consistency, and trajectory consistency are each weighted by 0\.5\. Stage II\.b further applies the backward landmark loss

ℒback=‖𝐞1\+𝐯b​\(𝐞1,1,𝐜\)−m⁡\(𝐜\)‖22,\\mathcal\{L\}\_\{\\mathrm\{back\}\}=\\left\\\|\\mathbf\{e\}\_\{1\}\+\\mathbf\{v\}\_\{b\}\(\\mathbf\{e\}\_\{1\},1,\\mathbf\{c\}\)\-m\(\\mathbf\{c\}\)\\right\\\|\_\{2\}^\{2\},\(16\)which trains terminal points to invert toward the deterministic center of the condition\-dependent start region\.

#### Inference\.

The primary endpoint is generated by one Euler step:

𝐞^1=𝐞0\+𝐯f​\(𝐞0,0,𝐜\)\.\\hat\{\\mathbf\{e\}\}\_\{1\}=\\mathbf\{e\}\_\{0\}\+\\mathbf\{v\}\_\{f\}\(\\mathbf\{e\}\_\{0\},0,\\mathbf\{c\}\)\.\(17\)ForM=8M\{=\}8stochastic starts, the resulting class logits are aggregated by log\-mean\-exp:

ℓ¯k=log⁡\(1M​∑j=1Mexp⁡\(ℓk\(j\)\)\)\.\\bar\{\\ell\}\_\{k\}=\\log\\\!\\left\(\\frac\{1\}\{M\}\\sum\_\{j=1\}^\{M\}\\exp\(\\ell\_\{k\}^\{\(j\)\}\)\\right\)\.\(18\)Samples with maximum A\-GCH probability below 0\.7 replace the one\-step endpoint with a three\-step Euler integration before geometric rescoring\.

### Geometric Evidence and Backward Compatibility

#### A\-GCH\.

The Adaptive Geometric Classification Head \(A\-GCH\) evaluates𝐞^1\\hat\{\\mathbf\{e\}\}\_\{1\}under each Gaussian prototype cloud\. Its raw Gaussian score contains both the squared Mahalanobis distance and the covariance normalization term:

gk=−12​dM2​\(𝐞^1,𝝁k,𝚺k\)−12​log​det\(𝚺k\)\.g\_\{k\}=\-\\frac\{1\}\{2\}d\_\{M\}^\{2\}\\\!\\left\(\\hat\{\\mathbf\{e\}\}\_\{1\};\\boldsymbol\{\\mu\}\_\{k\},\\boldsymbol\{\\Sigma\}\_\{k\}\\right\)\-\\frac\{1\}\{2\}\\log\\det\(\\boldsymbol\{\\Sigma\}\_\{k\}\)\.\(19\)At inference, conflict\-adaptive temperature scaling gives

ℓkfwd=gkτ⁡\(𝐜\),τ⁡\(𝐜\)=τ0​\(1\+η​max⁡\{0,E~ψ\}\)\.\\ell\_\{k\}^\{\\mathrm\{fwd\}\}=\\frac\{g\_\{k\}\}\{\\tau\(\\mathbf\{c\}\)\},\\qquad\\tau\(\\mathbf\{c\}\)=\\tau\_\{0\}\\bigl\(1\+\\eta\\max\\\{0,\\widetilde\{E\}\_\{\\psi\}\\\}\\bigr\)\.\(20\)The transported endpoint is directly supervised by

ℒclsflow=CE⁡\(\{gk\}k=1K,y\),\\mathcal\{L\}\_\{\\mathrm\{cls\}\}^\{\\mathrm\{flow\}\}=\\mathrm\{CE\}\\bigl\(\\\{g\_\{k\}\\\}\_\{k=1\}^\{K\},y\\bigr\),\(21\)so the flow field learns endpoints that are likely under the correct adaptive cloud\.

#### BGD\.

Forward scoring identifies the prototype cloud that best explains𝐞^1\\hat\{\\mathbf\{e\}\}\_\{1\}\. Bidirectional Generative Decision \(BGD\) provides a backward compatibility score indicating whether the mean of a candidate class can invert toward the condition\-dependent start region\. For each classkk,

𝐞^0\(k\)=𝝁k\+𝐯b​\(𝝁k,1,𝐜\),\\hat\{\\mathbf\{e\}\}\_\{0\}^\{\(k\)\}=\\boldsymbol\{\\mu\}\_\{k\}\+\\mathbf\{v\}\_\{b\}\(\\boldsymbol\{\\mu\}\_\{k\},1,\\mathbf\{c\}\),\(22\)and its consistency with the conditional\-prior center is scored by

ℓkbwd=−‖𝐞^0\(k\)−m⁡\(𝐜\)‖222​τback\.\\ell\_\{k\}^\{\\mathrm\{bwd\}\}=\-\\frac\{\\left\\\|\\hat\{\\mathbf\{e\}\}\_\{0\}^\{\(k\)\}\-m\(\\mathbf\{c\}\)\\right\\\|\_\{2\}^\{2\}\}\{2\\tau\_\{\\mathrm\{back\}\}\}\.\(23\)Thus, them⁡\(𝐜\)m\(\\mathbf\{c\}\)marker in Figure[1](https://arxiv.org/html/2609.27615#Sx3.F1)is the deterministic reference shared by the stochastic forward starts and the class\-specific backward reconstructions\. Accordingly,𝐞^1\\hat\{\\mathbf\{e\}\}\_\{1\}supplies the forward A\-GCH branch, whereas each pair\(𝝁k,𝐜\)\(\\boldsymbol\{\\mu\}\_\{k\},\\mathbf\{c\}\)supplies the backward BGD branch\. BGD introduces no additional trainable parameters or class\-wise objective; it reuses the learned backward field to construct this inference\-time compatibility score\. Final logits combine both channels in log space:

ℓk=ℓkfwd\+λback​ℓkbwd,\\ell\_\{k\}=\\ell\_\{k\}^\{\\mathrm\{fwd\}\}\+\\lambda\_\{\\mathrm\{back\}\}\\,\\ell\_\{k\}^\{\\mathrm\{bwd\}\},\(24\)withλback=0\.5\\lambda\_\{\\mathrm\{back\}\}\{=\}0\.5and temperatureτback=2\\tau\_\{\\mathrm\{back\}\}\{=\}2selected on validation\. The final score favors classes whose cloud explains the transported endpoint and whose mean reconstructs the original condition\-dependent region\.

### Training Objective and Curriculum

Training activates evidence construction, transport, and inverse\-flow refinement in sequence\. Stage I learns the variational emotion factors using the CGD\-IB objective described above\. Stage II\.a retains this factorization supervision and introduces ECA, bidirectional flow matching, trajectory consistency, prototype\-cloud classification, and memory\-bank updates\. Stage II\.b activates the additional N3 conflict pairs and backward landmark supervision to refine terminal inversion\. Each stage optimizes only the objectives activated at that stage; BGD adds no separate training loss\. Table[2](https://arxiv.org/html/2609.27615#Sx3.T2)summarizes the curriculum\.

Table 2:Three\-stage training curriculum\.

## Experiments

Table 3:Audio\-text MER comparison on four\-class IEMOCAP and seven\-class MELD\. BiCFlow\-MER uses five\-fold speaker\-independent training and evaluation over the five IEMOCAP sessions; reported IEMOCAP values are the mean±\\pmstandard deviation across the five held\-out\-session folds\. MELD results follow the official train/development/test splits on MELD\. Best results are bolded and second\-best results are underlined\.### Experimental Setup

#### Dataset and protocol\.

Evaluation is conducted on four\-class IEMOCAP\([Busso et al\. 2008](https://arxiv.org/html/2609.27615#bib.bib1)\): angry, happy \(merged excited/happy\), sad, and neutral, under the utterance\-level audio\-text setting\. We use five\-fold speaker\-independent evaluation over its five sessions, training on four sessions and testing on the held\-out session\. We also evaluate BiCFlow\-MER on MELD\([Poria et al\. 2019](https://arxiv.org/html/2609.27615#bib.bib21)\)under the seven\-class setting with its official train/development/test splits\. Metrics are unweighted accuracy \(UA\), weighted accuracy \(WA\), and weighted F1 \(W\-F1\); MELD results are reported with WA and W\-F1, with W\-F1 as the main metric\.

#### Modalities\.

For IEMOCAP and MELD, BiCFlow\-MER encodes audio with WavLM\-Large and text with DeBERTa\-v3\-base\. Each utterance is classified independently without visual features, speaker\-identity metadata, or conversational context; unless stated otherwise, ablations use the same bimodal input\.

#### Implementation details\.

For IEMOCAP and MELD, audio is resampled to 16 kHz mono and transcripts are tokenized with the DeBERTa vocabulary\. WavLM\-Large and DeBERTa\-v3\-base are used with LoRA rank 16, flow dimensiond=64d\{=\}64,λclsflow=7\\lambda\_\{\\mathrm\{cls\}\}^\{\\mathrm\{flow\}\}\{=\}7,σmax=0\.1\\sigma\_\{\\max\}\{=\}0\.1,λback​\_​land=0\.3\\lambda\_\{\\mathrm\{back\\\_land\}\}\{=\}0\.3,τ0=1\\tau\_\{0\}\{=\}1,η=0\.5\\eta\{=\}0\.5, andτback=2\\tau\_\{\\mathrm\{back\}\}\{=\}2unless noted\. Within CGD\-IB,λcf=0\.5\\lambda\_\{\\mathrm\{cf\}\}\{=\}0\.5andλE=1\\lambda\_\{E\}\{=\}1;βIB\\beta\_\{\\mathrm\{IB\}\}increases linearly from 0\.01 to 0\.1 during Stage I and then decreases linearly to 0\.02 across Stages II\.a–II\.b\. Training uses AdamW \(learning rate2×10−42\\times 10^\{\-4\}, weight decay 0\.01\), effective batch size 32, and exponential moving average \(EMA\) decay 0\.999\. All experiments were run on a single NVIDIA A100 GPU with 80 GB of memory\. Unless stated otherwise, BiCFlow\-MER and its controlled variants are trained using the three\-stage curriculum in Table[2](https://arxiv.org/html/2609.27615#Sx3.T2)\.

#### Inference calibration\.

Using only the validation split, we fit calibrated logitsℓkcal=ℓk/T\+bk\\ell\_\{k\}^\{\\mathrm\{cal\}\}=\\ell\_\{k\}/T\+b\_\{k\}, whereTTis a shared temperature and the per\-class biasesbkb\_\{k\}are initialized from training\-set log\-frequencies\. Both are selected by validation UA and frozen for testing\.

#### Comparison with representative methods\.

Table[3](https://arxiv.org/html/2609.27615#Sx4.T3)compares BiCFlow\-MER with recent audio\-text MER baselines, including GateM2Former \(GM2F\)\([Khurana et al\. 2022](https://arxiv.org/html/2609.27615#bib.bib32);[Zhang et al\. 2023](https://arxiv.org/html/2609.27615#bib.bib33);[Xu et al\. 2025](https://arxiv.org/html/2609.27615#bib.bib34);[Zhang and Li 2023](https://arxiv.org/html/2609.27615#bib.bib35);[Hou et al\. 2023](https://arxiv.org/html/2609.27615#bib.bib36);[Shao et al\. 2025](https://arxiv.org/html/2609.27615#bib.bib37);[Lei et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib38);[Han et al\. 2025](https://arxiv.org/html/2609.27615#bib.bib39)\)\. S and T indicate speech and text access; baseline values are taken from the corresponding literature\. BiCFlow\-MER ranks first on all four metrics, exceeding the second\-best values by 0\.40/0\.11 points on IEMOCAP WA/UA and 0\.55/1\.43 points on MELD WA/W\-F1\.

### Cross\-Dataset Evaluation on CASE

BiCFlow\-MER is further evaluated on Conflict in Acoustic\-Semantic Emotion \(CASE\)\([Huang et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib40)\), where acoustic emotion and lexical semantics may disagree\. Following the exact FAS protocol, BiCFlow\-MER is trained on the same IEMOCAP, CMU\-MOSEI, MER2024, MELD, RAVDESS, and ESD partitions and evaluated on the complete 378\-utterance CASE set\([Huang et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib40)\)\. CASE remains strictly zero\-shot, with no samples used for training, validation, calibration, or hyperparameter selection\. In the audio\-only CASE configuration, we follow the FAS codebase and use its frozen Whisper\-large\-v2 and MingTok\-Audio encoders to extract semantic\- and acoustic\-oriented features from each waveform\. The acoustic and semantic streams instantiate the originalaaandttbranches, respectively; all downstream modules, objectives, and settings remain unchanged, and the same frozen feature extractors are used for all controlled variants\. This branch assignment does not introduce textual input: both streams are extracted from the same waveform\. Accordingly, Aco\. and Sem\. in Table[4](https://arxiv.org/html/2609.27615#Sx4.T4)describe the dominant information preserved by each representation rather than distinct input modalities\. No transcript encoder or textual token sequence is used in the CASE experiment\. Following the released FAS evaluation implementation, W\-F1 is computed using class\-support weighting\. Table[4](https://arxiv.org/html/2609.27615#Sx4.T4)reports 61\.90% accuracy \(ACC\) and 59\.82% W\-F1, exceeding Fusion Acoustic\-Semantic \(FAS\)\([Huang et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib40)\)by 2\.52 and 4\.74 points, respectively\. The remaining pretrained baselines peak at 47\.26% ACC and 44\.97% W\-F1, leaving FAS and BiCFlow\-MER as a distinct upper tier\. Under the strictly zero\-shot protocol, these results establish end\-to\-end transfer to unseen acoustic\-semantic conflicts; Table[5](https://arxiv.org/html/2609.27615#Sx4.T5)attributes this transfer to individual evidence, transport, and scoring components\.

Table 4:Zero\-shot CASE comparison\. All methods use audio\-only input; Aco\. and Sem\. denote acoustic and semantic representation attributes\. Baseline results and annotations follow the original FAS study\([Huang et al\. 2026](https://arxiv.org/html/2609.27615#bib.bib40)\)\. Best values are bolded; second\-best values are underlined\.
### Analysis and Ablation

Table 5:Controlled variants on IEMOCAP \(audio\-text\) and zero\-shot CASE \(audio\-only semantic/acoustic streams\), with no CASE target\-set adaptation\. Best results are bolded; second\-best results are underlined\.Table 6:Modality ablation on IEMOCAP\.Figure 2:Qualitative stage\-wise organization on four\-class IEMOCAP\. Left: affective evidence conditions\. Middle: gray condition\-dependent flow starts, colored transported endpoints, and representative trajectories\. Right: adaptive prototypes \(stars\) and schematic two\-dimensional prototype neighborhoods \(dashed ellipses\)\.#### Stage\-wise emotion\-space organization\.

E1–E4 denote angry, happy, sad, and neutral, respectively\. The condition space retains local overlap, whereas CT\-BiRF maps condition\-dependent starts to endpoints evaluated against A\-GCH prototype neighborhoods\.

Figure 3:Validation UA after Stage I under the proposed curriculum and an abrupt\-activation baseline, which activates all Stage II components immediately after Stage I\. The proposed schedule introduces ECA, conditional transport, and geometric scoring in Stage II\.a, then adds N3 conflict pairs and backward landmark supervision in Stage II\.b\.
#### Curriculum behavior\.

The staged schedule reaches high validation UA earlier and remains more stable after Stage II\.b, supporting the proposed ordering\. The controlled variants below then replace each stage\-specific mechanism with a simpler counterpart to test its role in this sequence\.

#### Controlled variants\.

Table[5](https://arxiv.org/html/2609.27615#Sx4.T5)isolates the main design blocks through controlled replacements\. The w/o Fact\. variant uses ordinary fused evidence; w/o ECA replaces disagreement\-conditioned fusion with ordinary fusion; w/o CT\-BiRF retains the same pretrained encoders but replaces conditional transport with direct recognition; w/o A\-GCH removes adaptive prototype\-cloud scoring; and w/o BGD removes the inference\-time backward compatibility score\.

On CASE, w/o ECA causes the largest degradation, with losses of 7\.90 ACC and 6\.26 W\-F1 points; it also produces the largest IEMOCAP UA loss of 2\.67 points\. These results identify disagreement\-conditioned fusion as an important contributor on the conflict\-focused CASE benchmark\. The w/o Fact\., w/o CT\-BiRF, and w/o A\-GCH variants reduce CASE ACC/W\-F1 by 5\.03/5\.52, 4\.89/3\.38, and 4\.78/3\.85 points, respectively, supporting the roles of affect\-oriented factorization, conditional transport, and adaptive prototype geometry in zero\-shot transfer\. The w/o BGD variant produces a smaller but consistent CASE loss of 2\.25 ACC and 0\.96 W\-F1 points, showing that backward compatibility scoring provides an additional gain\.

#### Modality reliance\.

Table[6](https://arxiv.org/html/2609.27615#Sx4.T6)shows that the final condition benefits from complementary speech and text evidence rather than collapsing to a single dominant stream\. Speech alone reaches 73\.83±\\pm2\.05 WA and 75\.30±\\pm3\.31 UA, while text alone reaches 65\.75±\\pm1\.70 WA and 67\.56±\\pm2\.94 UA\. The audio\-text setting reaches 78\.18±\\pm1\.44% WA and 78\.90±\\pm2\.80% UA, improving on speech alone by 4\.35 and 3\.60 points, respectively\. CT\-BiRF transports𝐞0\\mathbf\{e\}\_\{0\}under the affective condition𝐜\\mathbf\{c\}rather than transporting𝐜\\mathbf\{c\}itself; the bimodal gains therefore show that complementary modalities improve the condition guiding transport\.

## Conclusion

BiCFlow\-MER addresses three evidence\-level challenges in audio\-text MER\. Emotion\-oriented factorization separates affective evidence from speaker\-style and lexical\-content factors, ECA incorporates audio\-text disagreement into condition construction, and conditional transport with forward geometry and backward compatibility scoring evaluates candidate emotions against both endpoint structure and the condition\-dependent start region\. Results on IEMOCAP and MELD establish standard recognition performance, while the zero\-shot CASE results and controlled variants identify how the complete evidence chain transfers under acoustic\-semantic conflict\. This formulation establishes a generative\-decision paradigm in which multimodal emotion evidence is explicitly constructed, transported, and verified\.

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